Question

How much would you have to

Answer 1

The principal sum to be deposited is $ 551.26

Solution:

Given that,

Amount after 10 years = $ 1000

Rate of Interest = 6 % compounded quarterly

Number of years = 10 years

Principal = ?

The formula for compound interest, including principal sum, is:

$A=p\left(1+\frac{r}{n}\right)^{n t}$

Where,

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

P = the principal investment amount (the initial deposit or loan 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

Since interest is compounded quarterly, n = 4

$r = 6 \% = \frac{6}{100} = 0.06$

Substituting the values in formula,

$\begin{aligned}&1000=p\left(1+\frac{0.06}{4}\right)^{4 \times 10}\\\\&1000=p(1+0.015)^{40}\\\\&1000=p(1.015)^{40}\\\\&1000=p \times 1.8140\\\\&p=\frac{1000}{1.8140}=551.26\end{aligned}$

Thus the principal sum to be invested is $ 551.26