A certificate of deposit is purchased for $3000 and held for 5 years. If the certificate earns 6% per annum, compounded quarterly, (four times per year) what is it worth at the end of the 5 years?
Question
A certificate of deposit is purchased for $3000 and held for 5 years. If the certificate earns 6% per annum, compounded quarterly, (four times per year) what is it worth at the end of the 5 years?
Solution
To calculate the future value of a Certificate of Deposit, we use the formula for compound interest:
A = P (1 + r/n) ^ nt
Where: A = the future value of the investment P = the principal investment amount (the initial deposit or loan amount) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = time the money is invested for in years
In this case: P = $3000 r = 6% or 0.06 n = 4 (compounded quarterly) t = 5 years
Substituting these values into the formula:
A = 3000 (1 + 0.06/4) ^ (4*5)
A = 3000 (1 + 0.015) ^ 20
A = 3000 (1.015) ^ 20
A = 3000 * 1.346855007
A = $4039.57
So, the Certificate of Deposit will be worth $4039.57 at the end of 5 years.
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