## How to Calculate and Solve for Present Worth | Gradient Series | Economic Equivalence The image above represents present worth.

To compute for present worth, three essential parameters are needed and these parameters are Gradient Amount (G), Interest Rate (i) and Number of Years (N).

The formula for calculating present worth:

P = G[((1 + i)N) – iN – 1] / [i²((1 + i)N)]

Where:

P = Present Amount or Worth
i = Interest Rate
N – Number of Years

Let’s solve an example;
Find the present worth when the gradient amount is 22, the interest rate is 0.2 and the number of years is 2.

This implies that;

G = Gradient Amount = 22
i = Interest Rate = 0.2
N – Number of Years = 2

P = G[((1 + i)N) – iN – 1] / [i²((1 + i)N)]
P = 22[((1 + 0.2)2) – 0.2(2) – 1] / [0.2²((1 + 0.2)2)]
P = 22[((1.2)2) – 0.4 – 1] / [0.0400000000000001((1.2)2)]
P = 22[1.44 – 0.4 – 1] / [0.04000000000000001 x 1.44]
P = 22[0.040000000000000036] / [0.05760000000000001]
P = 22 x 0.6944444444444449
P = 15.27

Therefore, the present worth is ₦15.27.

## How to Calculate and Solve for capital recovery | Equal Payment Series | Economic Equivalence The image above represents capital recovery.

To compute for capital recovery, three essential parameters are needed and these parameters are Present Amount or Worth (P), Interest Rate (i) and Number of Years (N).

The formula for calculating capital recovery:

A = P[i((1 + i)N)] / [((1 + i)N) – 1]

Where:

A = Annual Worth or Amount
P = Present Worth or Amount
i = Interest Rate
N = Number of Years

Let’s solve an example;
Find the annual worth when the present worth is 30, the interest rate is 0.2 and the number of years is 4.

This implies that;

P = Present Worth or Amount = 30
i = Interest Rate = 0.2
N = Number of Years = 4

A = P[i((1 + i)N)] / [((1 + i)N) – 1]
A = 30[0.2((1 + 0.2)4)] / [((1 + 0.2)4) – 1]
A = 30[0.2((1.2)4)] / [((1.2)4) – 1]
A = 30[0.2 x 2.0736] / [2.0736 – 1]
A = 30[0.41472] / [1.07359]
A = 30 x 0.386
A = 11.58

Therefore, the capital recovery is ₦11.58.

## How to Calculate and Solve for Present Worth | Equal Payment Series | Economic Equivalence The image above represent present worth.

To compute for present worth, three essential parameters are needed and these parameters are Annual Amount or Worth (A), Interest Rate (i) and Number of Years (N).

The formula for calculating present worth:

P = A[((1 + i)N) – 1] / [i((1 + i)N)]

Where:

P = Present Worth or Amount
A = Annual Worth or Amount
i = Interest Rate
N = Number of Years

Let’s solve an example;
Given that the annual worth is 29, the interest rate is 0.2 and the number of years is 10. Find the present worth?

This implies that;

A = Annual Worth or Amount = 29
i = Interest Rate = 0.2
N = Number of Years = 10

P = A[((1 + i)N) – 1] / [i((1 + i)N)]
P = 29[((1 + 0.2)10) – 1] / [0.2((1 + 0.2)10)]
P = 29[((1.2)10) – 1] / [0.2((1.2)10)]
P = 29[6.191 – 1] / [0.2 x 6.191]
P = 29[5.191] / [1.238]
P = 29 x 4.19
P = 121.58

Therefore, the present worth is ₦121.58.

## How to Calculate and Solve for Sinking Fund | Equal Payment Series | Economic Equivalence The image above represents sinking fund.

To compute for sinking fund, three essential parameters are needed and these parameters are Future Amount or Worth (F), Interest Rate (i) and Number of Years (N).

The formula for calculating sinking fund:

A = Fi / [((1 + i)N) – 1]

Where:

A = Annual Worth or Amount
F = Future Worth or Compound Amount
i = Interest Rate
N = Number of Years

Let’s solve an example;
Find the sinking fund when the future worth is 28, the interest rate is 0.2 and the number of years is 11.

This implies that;

F = Future Worth or Compound Amount = 28
i = Interest Rate = 0.2
N = Number of Years = 11

A = Fi / [((1 + i)N) – 1]
A = 28(0.2) / [((1 + 0.2)11) – 1]
A = 28(0.2) / [((1.2)11) – 1]
A = 28(0.2) / [(7.43) – 1]
A = 28(0.2) / [6.43]
A = 28 x 0.0311
A = 0.87

Therefore, the sinking fund is ₦0.87.

## How to Calculate and Solve for Future Worth | Equal Payment Series | Economic Equivalence The image above represents future worth.

To compute for future worth, three essential parameters are needed and these parameters are Annual Amount or Worth (A), Interest Rate (i) and Number of Years (N).

The formula for calculating future worth:

F = A[((1 + i)N) – 1] / i

Where;

F = Future Worth or Amount
A = Annual Worth or Amount
i = Interest Rate
N = Number of Years

Let’s solve an example;
Find the future worth when the annual worth is 21, the interest rate is 0.2 and the number of years is 9.

This implies that;

A = Annual Worth or Amount = 21
i = Interest Rate = 0.2
N = Number of Years = 9

F = A[((1 + i)N) – 1] / i
F = 21[((1 + 0.2)9) – 1] / 0.2
F = 21[((1.2)9) – 1] / 0.2
F = 21[5.159 – 1] / 0.2
F = 21[4.159] / 0.2
F = 21 x 20.79
F = 436.77

Therefore, the future worth is ₦436.77.

## How to Calculate and Solve for Future Worth | Simple Payment | Economic Equivalence The image above represents future worth.

To compute for future worth, three essential parameters are needed and these parameters are Present Amount or Worth (P), Interest Rate (i) and Number of Years (N).

The formula for calculating future worth:

F = P(1 + i)N

Where:

F = Compound Amount or Future Worth
P = Present Amount or Worth
i = Interest Rate
N = Number of Years

Let’s solve an example;
Find the future worth when the present worth is 12, the interest rate is 0.2 and the number of years is 10.

This implies that;

P = Present Amount or Worth = 12
i = Interest Rate = 0.2
N = Number of Years = 10

F = P(1 + i)N
F = 12(1 + 0.2)10
F = 12(1.2)10
F = 12(6.19)
F = 74.30

Therefore, the future worth is ₦74.30.

## How to Calculate and Solve for Present Worth | Simple Payment | Economic Equivalence The image above represents present worth.

To compute for present worth, three essential parameters are needed and these parameters are Future Amount or Worth (F), Interest Rate (i) and Number of Years (N).

The formula for calculating present worth:

P = F / (1 + i)N

Where:

P = Present Worth or Amount
F = Future Worth or Compound Amount
i = Interest Rate
N = Number of Years

Let’s solve an example;
Find the present worht when the future amount or worth is 24, the interest rate is 0.06 and the number of years is 11.

This implies that;

F = Future Worth or Compound Amount = 24
i = Interest Rate = 0.06
N = Number of Years = 11

P = F / (1 + i)N
P = 24 / (1 + 0.06)11
P = 24 / (1.06)11
P = 24 / 1.89
P = 12.64

Therefore, the present worth is ₦12.64.

## How to Calculate and Solve for Depreciation Value | Declining Balance Method | Depreciation The image above represents depreciation value.

To compute for depreciation value, three essential parameters are needed and these are Present Amount or Worth (P), Rate of Depreciation (α) and Number of Years of the Asset (t).

The formula for calculating depreciation value:

D = Pα(1 – α)(t – 1)

Where:

D = Depreciation Value
P = Present worth or amount
t = Number of years of the asset
α = rate of depreciation

Let’s solve an example;
Find the depreciation value when the present amount or worth is 14, the rate of depreciation is 2 and the number of years of the asset is 10.

This implies that;

P = Present worth or amount = 14
t = Number of years of the asset = 10
α = rate of depreciation = 2

D = Pα(1 – α)(t – 1)
D = 14(2)(1 – 2)(10 – 1)
D = 14(2)(-1)9
D = 14(2)(-1)
D = -28

Therefore, the depreciation value is ₦ -28.

Calculating the Present Amount or Worth when the Depreciation Value, the Rate of Depreciation and the Number of Years of the Asset is Given.

P = D / α (1 – α)(t – 1)

Where;

P = Present worth or amount
D = Depreciation Value
t = Number of years of the asset
α = rate of depreciation

Let’s solve an example;
Find the present amount or worth when the depreciation value is 40, the rate of depreciation is 10 and the number of years of the asset is 9.

This implies that;

D = Depreciation Value = 40
t = Number of years of the asset = 9
α = rate of depreciation = 10

P = D / α (1 – α)(t – 1)
P = 40 / 10 (1 – 10)(9 – 1)
P = 40 / 10 (- 9)(8)
P = 40 / 10 (- 43046721)
P = 40 / – 430467210
P = 9.29e-8

Therefore, the present amount or worth is 9.29e-8.

## How to Calculate and Solve for Book Value | Declining Balance Method | Depreciation The image above represents book value.

To compute for book value, three essential parameters are needed and these parameters are Present Amount or Worth (P), Rate of Depreciation (α) and Number of Years of the Asset (t).

The formula for calculating book value:

B = P(1 – α)t

Where:

B = Book value of an asset
P = Present worth or amount
α = rate of depreciation
t = Number of years of the asset

Let’s solve an example;
Find the book value when the present amount or worth is 8, the rate of depreciation is 18 and the number of years of the asset is 10.

This implies that;

P = Present worth or amount = 8
α = rate of depreciation = 18
t = Number of years of the asset = 10

B = P(1 – α)t
B = 8(1 – 18)10
B = 8(-17)10
B = 8 x 201
B = 1612

Therefore, the book value is ₦1612.

Calculating the Present Amount or Worth when the Book Value, the Rate of Depreciation and the Number of Years of the Asset is Given.

P = B / (1 – α)t

Where;

P = Present worth or amount
B = Book value of an asset
α = rate of depreciation
t = Number of years of the asset

Let’s solve an example;
Find the present amount or worth when the book value is 32, the rate of depreciation is 16 and the number of years of the asset is 10.

This implies that;

B = Book value of an asset = 32
α = rate of depreciation = 16
t = Number of years of the asset = 10

P = B / (1 – α)t
P = 32 / (1 – 16)10
P = 32 / (- 15)10
P = 32 / 5766
P = 0.00554

Therefore, the present amount or worth is 0.00554.

## How to Calculate and Solve for Depreciation Value | Straight line Method | Depreciation The image above represents depreciation value.

To compute for depreciation value, three essential value are needed and these parameters are Present Amount or Worth (P), Salvage Value (S) and Total Estimated Life of the Asset (N).

The formula for calculating depreciation value:

D = (P – S) / N

Where:

P = Present worth or amount
N = Total estimated life of an asset
S = Salvage value

Let’s solve an example;
Find the depreciation value when the present amount or worth is 9, the salvage value is 4 and the total estimated life of an asset is 10.

This implies that;

P = Present worth or amount = 9
N = Total estimated life of an asset = 10
S = Salvage value = 4

D = (P – S) / N
D = (9 – 4) / 10
D = 5 / 10
D = 0.5

Therefore, the depreciation value is ₦0.5.

Calculating the Present Amount or Worth when the Depreciation Value, the Total Estimated life of an Asset and the Salvage Value is Given.

P = (D x N) + S

Where;

P = Present worth or amount
D = Depreciation Value
N = Total estimated life of an asset
S = Salvage value

Let’s solve an example;
Find the present amount or worth when the depreciation value is 22, the total estimated life of an asset is 12 and the salvage value is 8.

This implies that;

D = Depreciation Value = 22
N = Total estimated life of an asset = 12
S = Salvage value = 8

P = (D x N) + S
P = (22 x 12) + 8
P = 264 + 8
P = 272

Therefore, the present amount or worth is 272.