When Lisa and Tom had their first child, they put $7,500 into a savings account that earns 6% compound interest. If Lisa and Tom did not add or remove anything from the savings account, how much interest will they have earned after 4 years? Round to the nearest hundredth of a cent. (the answer is not 1,936.07)
To calculate the compound interest earned after 4 years, we use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal (initial deposit)
r = annual interest rate (in decimal form)
n = number of times the interest is compounded per year
t = number of years
Plugging in the values we have:
P = $7,500
r = 6% = 0.06
n = 1 (compounded annually)
t = 4 years
A = $7,500(1 + 0.06/1)^(1*4)
A = $7,500(1.06)^4
A = $7,500(1.262476)
A ≈ $9,437.82
To find the total interest earned, we subtract the initial principal from the future value:
Interest = $9,437.82 - $7,500
Interest ≈ $1,937.82
Therefore, after 4 years, Lisa and Tom will have earned approximately $1,937.82 in compound interest.