How to Calculate and Solve for Annual Worth | Gradient Series | Economic Equivalence

The image above represents annual worth.

To compute for annual 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 annual worth:

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

Where:

A = Annual Amount or Worth (Conversion Factor)
G = Gradient amount
i = Interest Rate
N = Number of Years

Let’s solve an example;
Find the annual worth when the gradient amount is 11, the interest rate is 0.2 and the number of years is 12.

This implies that;

G = Gradient amount = 11
i = Interest Rate = 0.2
N = Number of Years = 12

A = G[((1 + i)N) – iN – 1] / [((1 + i)N) – 1]
A = 11[((1 + 0.2)12) – 0.2(12) – 1] / [((1 + 0.2)12) – 1]
A = 11[((1.2)12) – 2.40 – 1] / [((1.2)12) – 1]
A = 11[8.916 – 2.40 – 1] / [8.916 – 1]
A = 11[5.516] / [7.916]
A = 11 x 0.696
A = 7.66

Therefore, the annual worth is ₦7.66.

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How to Calculate and Solve for Present Worth | Geometric Gradient | Economic Equivalence

The image above represents present worth.

To compute for present worth, four essential parameters are needed and these parameters are First Payment (A1), Interest Rate (i), Number of Year(s) (N) and Percentage change in payment (g).

The formula for calculating present worth:

P = A₁[1 – ((1 + g)N)((1 + i)-N)] / [1 – g]

Where:

P = Present Worth or Amount
A₁ = First Payment
i = Interest Rate
g = Percentage change in payment
N = Number of Years

Let’s solve an example;
Find the present worth when the first payment is 10, the interest rate is 0.2, the percentage change in payment is 20 and the number of years is 5.

This implies that;

A₁ = First Payment = 10
i = Interest Rate = 0.2
g = Percentage change in payment = 20
N = Number of Years = 5

P = A₁[1 – ((1 + g)N)((1 + i)-N)] / [1 – g]
P = 10[1 – ((1 + 20)5)((1 + i)-(5))] / [1 – 20]
P = 10[1 – ((21)5)((1.2)-5)] / [-19]
P = 10[1 – (4084101)(0.401)] / [-19]
P = 10[1 – 1641308.59] / [-19]
P = 10[-1641307.59] / [-19]
P = 10 x 86384.610
P = 863846.10

Therefore, the present worth is ₦863846.10.

Continue reading How to Calculate and Solve for Present Worth | Geometric Gradient | Economic Equivalence

How to Calculate and Solve for Present Worth | Geometric Gradient | Economic Equivalence

The image above represents present worth.

To compute for present worth, three essential parameters are needed and these parameters are First Payment (A1), Interest Rate (i) and Number of Year(s) (N).

The formula for calculating present worth:

P = A₁[N / (1 + i)]

Where:

P = Present Worth or Amount
A₁ = First Payment
i = Interest Rate
N = Number of Years

Let’s solve an example;
Find the present worth when the first payment is 8, the interest rate is 0.3 and the number of years is 22.

This implies that;

A₁ = First Payment = 8
i = Interest Rate = 0.3
N = Number of Years = 22

P = A₁[N / (1 + i)]
P = 8[22 / (1 + 0.3)]
P = 8[22 / 1.3]
P = 8 x 16.92
P = 135.38

Therefore, the present worth is ₦135.38.

Continue reading How to Calculate and Solve for Present Worth | Geometric Gradient | Economic Equivalence

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:

G = Gradient Amount
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.

Continue reading How to Calculate and Solve for Present Worth | Gradient Series | Economic Equivalence

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.

Continue reading How to Calculate and Solve for capital recovery | Equal Payment Series | Economic Equivalence

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.

Continue reading How to Calculate and Solve for Present Worth | Equal Payment Series | Economic Equivalence

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.

Continue reading How to Calculate and Solve for Sinking Fund | Equal Payment Series | Economic Equivalence

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.

Continue reading How to Calculate and Solve for Future Worth | Equal Payment Series | Economic Equivalence

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.

Continue reading How to Calculate and Solve for Future Worth | Simple Payment | Economic Equivalence

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.

Continue reading How to Calculate and Solve for Present Worth | Simple Payment | Economic Equivalence