Question

Nancy opened a savings account 7 years ago. The account earns 5% interest, compounded quarterly. If the current balance is $1,000.00, how much did she deposit initially?

Answer 1

The amount deposited initially is $ 706.22

Solution:

The formula for amount using compound interest is given as:

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

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

From given,

t = 7 years

A = 1000

P = ?

$r = 5 \% = \frac{5}{100} = 0.05$

n = 4 (since compounded quarterly)

Substituting the values we get,

$1000 = p(1+\frac{0.05}{4})^{4 \times 7}\\\\1000 = p(1+\frac{0.05}{4})^{28}\\\\1000 = p(1+0.0125)^{28}\\\\1000 = p(1.0125)^{28}\\\\1000 = p \times 1.4159923\\\\p = \frac{1000}{1.4159923}\\\\p = 706.2185 \approx 706.22$

Thus amount deposited initially is $ 706.22