Answer:
2. $19,547.04
3. $10,276.54
4. $16,758.38
Explanation:
You have three problems in compound interest with different initial payments, interest rates, and compounding intervals. You want the relationship between the initial payment and the future value.
Future value multiplier
The multiplier of a single payment earning annual interest rate r compounded n times per year for t years is ...
k = (1 +r/n)^(nt)
2.
For this problem, r=0.09, n=1, t=9. The multiplier of the payment is ...
k = (1 +0.09/1)^(1·9) = 1.09^9 = 2.17189328
Then the future value of $9000 will be ...
FV = $9000 × 2.17189328 ≈ $19,547.04
3.
For this problem, r=0.10, n=12, t=4. The multiplier of the payment is ...
k = (1 +0.10/12)^(12·4) = 1.08333...^48 = 1.48935410
Then the future value of $6900 will be ...
FV = $6900 × 1.48935410 ≈ $10,276.54
4.
For this problem, r=0.13, n=12, t=13. The multiplier of the payment is ...
k = (1 +0.13/12)^(12·13) = 1.0108333...^156 = 5.3704484
Then the payment that gives a future value of $90,000 will be ...
P = $90,000/5.3704484 = $16,758.38
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Additional comment
For the spreadsheet calculation, we used the "Goal Seek" capability to adjust the value of cell F4 to 90000 by changing the value in cell B4.
We could have calculated the multiplier as above, then used it different ways for the different problems. Instead, we used one FV( ) function for all of the problems.