John works part-time and earns $400 each month. He deposits his earnings at the end of each month in an account which pays 5.9% compounded monthly. If he does this consistently for three years, how much will he have?
To calculate the future value of John's earnings over three years, we need to use the compound interest formula:
A = P(1 + r/n)^(nt)
where:
A = the future value of the investment
P = the principal amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case:
P = John's monthly earnings = $400
r = 5.9% = 0.059 (as a decimal)
n = 12 (compounded monthly)
t = 3 years
Plugging in these values into the formula, we get:
A = 400(1 + 0.059/12)^(12*3)
= 400(1 + 0.0049167)^(36)
≈ 400(1.0049167)^36
Calculating the exponential term, we get:
A ≈ 400(1.1790645)
A ≈ $471.63
After three years of consistently depositing $400 each month, John will have approximately $471.63 in his account.