Question

After 6 years, Naomi has approximately $3618.25 in her savings account. If her interest rate was 5% compounded annually, how much did she originally deposit into the account. Round answer to nearest dollar.

Answer 1

To calculate the original deposit amount, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the final amount in the account

P is the principal amount (initial deposit)

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the number of years

Given:

A = $3618.25

r = 5% = 0.05 (as a decimal)

n = 1 (compounded annually)

t = 6 years

1. Rearrange the formula to solve for P:

P = A / (1 + r/n)^(nt)

2. Plug in the values into the formula:

P = 3618.25 / (1 + 0.05/1)^(1*6)

3. Simplify inside the parentheses:

P = 3618.25 / (1.05)^(6)

4. Calculate the exponent:

P = 3618.25 / (1.34009601)

5. Divide the final amount by the result:

P = $2700.02

Therefore, Naomi originally deposited approximately $2700.02 into her savings account in order to have approximately $3618.25 after 6 years with an annual interest rate of 5% compounded annually. Rounded to the nearest dollar, the original deposit amount is $2700.