The formula for calculating the amount of money returned for an initial deposit into a
bank account or CD (certificate of deposit) is given by
nt
n
r
P A „Ê„Ë
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ƒ 1ƒy
A is the amount of the return.
P is the principal amount initially deposited.
r is the annual interest rate (expressed as a decimal).
n is the number of compound periods in one year.
t is the number of years.
Carry all calculations to six decimal places on each intermediate step, then round the
final answer to the nearest whole cent.
Suppose you deposit $2,000 for 5 years at a rate of 8%.
a) Calculate the return (A) if the bank compounds annually (n = 1). Round your
answer to the nearest whole cent.
Using more conventional online notation,
A = P(1+r/n)^nt
A = 2000(1.08)^5 = 2000*1.469328 = 2938.656 or 2938.66
To calculate the return (A) for a deposit at a rate of 8% compounded annually for 5 years, you will use the formula:
A = P(1 + r/n)^(nt)
where:
A is the amount of the return
P is the principal amount initially deposited ($2,000 in this case)
r is the annual interest rate (8%, expressed as a decimal, so r = 0.08)
n is the number of compound periods in one year (since it is compounded annually, n = 1)
t is the number of years (5 years in this case)
Now let's substitute the given values into the formula and calculate the return (A):
A = 2000(1 + 0.08/1)^(1*5)
A = 2000(1 + 0.08)^5
A = 2000(1.08)^5
A ≈ 2000(1.46933)
A ≈ 2938.66
Therefore, the return (A) if the bank compounds annually (n = 1) would be approximately $2,938.66.