Test Index

Time Value of Money

Question : 66 of 99

Marks: +1, -0

8\%

Solution:

Concept:

Future value of an ordinary annuity: payments at end of each period.

Explanation:

Monthly interest rate

i = \frac{8\%}{12} = \frac{0.08}{12} = \frac{1}{150}

Number of payments

n = 10

Payment amount

P = 500

Future value formula:

FV = P \cdot \frac{(1+i)^n - 1}{i}

First, compute

(1+i)^{10} = \left(1 + \frac{1}{150}\right)^{10} = \left(\frac{151}{150}\right)^{10}

Using binomial expansion:

(1+\frac{1}{150})^{10} \approx 1 + 10\cdot\frac{1}{150} + 45\cdot\frac{1}{150^2} + 120\cdot\frac{1}{150^3} + \cdots

1 + 0.06666667 + 0.002 + 0.00003556 = 1.06870223

(neglect higher terms)

Then

\frac{(1+i)^{10} - 1}{i} = \frac{0.06870223}{1/150} = 0.06870223 \times 150 = 10.3053345

Multiply by

P

FV = 500 \times 10.3053345 = 5152.66725 \approx 5152.70

Thus the future value after 10 payments is Rs. 5152.70.

Answer:

Option A: Rs. 5152.70

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