Answer to Question #90022 in Financial Math for Mahnoor Riaz

Question

If an employee deposits Rs. 2,000 at the end of each year into his company’s plan which pays 7% interest compounded quarterly, how much will he have in the account at the end of 5 years?

Answer 1

The formula for compound interest

$$A=P(1+{r \over n})^{nt}$$

A= the future value of the investment/loan, including interest

P = the principal investment amount

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per unit t

t = the time the money is invested or borrowed for

We have that $P_0=2000, r=0.07, n=4$

$$A_2=P_0\Big(1+(1+{r \over n})^n \Big)$$ $$A_3=P_0\Big(1+(1+{r \over n})^n+(1+{r \over n})^{2n} \Big)$$

We see the geometric series

$$S_k=1\cdot{1-\Big((1+{r \over n})^n \Big) ^k\over 1-(1+{r \over n})^n}$$

Then

$$A_m=P_0S_m=P_0\cdot{1-\Big((1+{r \over n})^n \Big) ^m\over 1-(1+{r \over n})^n}$$

How much will he have in the account at the end of 5 years?

$$A_6=2000\cdot{1-\Big((1+{0.07 \over 4})^4 \Big) ^6\over 1-(1+{0.07 \over 4})^4}=14373.78$$

He will have in the account at the end of 5 years RM 14373.78.