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+(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 \% = (5)/(100) = 0.05`

n = 4 (since compounded quarterly)

Substituting the values we get,

`1000 = p(1+(0.05)/(4))^(4 * 7)\\\\1000 = p(1+(0.05)/(4))^(28)\\\\1000 = p(1+0.0125)^(28)\\\\1000 = p(1.0125)^(28)\\\\1000 = p * 1.4159923\\\\p = (1000)/(1.4159923)\\\\p = 706.2185 \approx 706.22`

Thus amount deposited initially is $ 706.22