Question

A savings account earns 8% interest each year, compounded quarterly (4 times a year). If a person invests $100 and make no further deposits or withdrawals, what is the balance in the account after 3 years ​

Answer 1

The balance in account after 3 years is $ 126.82

Solution:

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

$A = p(1+\frac{r}{n})^{nt}$

Where,

A = the future value of the investment

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

From given,

p = 100

t = 3 years

r = 8 % = 8/100 = 0.08

n = 4 times

Therefore,

$A = 100(1 + \frac{0.08}{4})^{4 \times 3}\\\\A = 100( 1 + 0.02)^{12}\\\\A = 100(1.02)^{12}\\\\A = 100 \times 1.2682\\\\A = 126.82$

Thus the balance in account after 3 years is $ 126.82