Starting on her 21st birthday and continuing on every birthday up to and including her 65th, Jessie deposits $2,000 a year into an IRA. How much (to the nearest tenth) will be in the account on Jessie's 65th birthday if the account earns:
A. 7% compounded annually?
B. or 11% compounded annually?
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To find out how much will be in the account on Jessie's 65th birthday, we can use the future value (FV) formula for a series of equal deposits. The formula is:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future Value
P = Annual deposit amount
r = Interest rate per compounding period
n = Number of compounding periods
A. 7% compounded annually:
For 7% interest compounded annually, we have:
P = $2,000
r = 0.07 (7% expressed as a decimal)
n = 65 - 21 = 44 (since deposits start at 21 and continue up to and including the 65th birthday)
Plugging these values into the formula, we get:
FV = $2,000 * [(1 + 0.07)^44 - 1] / 0.07
Now, let's calculate it.