Jane wants to save for a trip to Canada. She will need $12,000 at the end of year 4. She can invest a certain amount at the end of each of the next four years in a bank account that will pay her 6.8 percent annually. How much will she have to invest annually to reach her target? (Round to the nearest dollar.)a.$2,538b.$2,711c.$3,000d.None of them.e.$2,980
Question
Jane wants to save for a trip to Canada. She will need 2,538b.3,000d.None of them.e.$2,980
Solution
The correct answer is a. $2,538.
This is an ordinary annuity problem where we know the future value (FV), the interest rate (r), and the number of periods (n), and we want to find out the annual payment (PMT).
The formula for the future value of an ordinary annuity is:
FV = PMT * [((1 + r)^n - 1) / r]
We can rearrange this formula to solve for PMT:
PMT = FV / [((1 + r)^n - 1) / r]
Substituting the given values into this formula gives:
PMT = $12,000 / [((1 + 0.068)^4 - 1) / 0.068]
Calculating this gives an annual payment of approximately $2,538.
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