A certificate of deposit is purchased for $3000 and held for 9 years. If the certificate earns 9% per annum, compounded quarterly, (four times per year) what is it worth at the end of the 9 years?
Question
A certificate of deposit is purchased for $3000 and held for 9 years. If the certificate earns 9% per annum, compounded quarterly, (four times per year) what is it worth at the end of the 9 years?
Solution
To solve this problem, we will use the formula for compound interest which is:
A = P (1 + r/n)^(nt)
Where: A = the amount of money accumulated after n years, including interest. P = the principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = the time the money is invested for in years
In this case: P = $3000 r = 9% or 0.09 (in decimal) n = 4 (since the interest is compounded quarterly) t = 9 years
Substituting these values into the formula, we get:
A = 3000 (1 + 0.09/4)^(4*9)
Now, calculate the expression inside the brackets:
= 3000 (1 + 0.0225)^(36)
= 3000 (1.0225)^(36)
Now, calculate the power:
= 3000 * 2.459814
Finally, multiply the principal amount by the result:
= $7379.44
So, the certificate of deposit is worth $7379.44 at the end of the 9 years.
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