Answer:
- $5957.95
- $408.35
Explanation:
You want to find the future value of an ordinary annuity with 5 annual payments of $1100 earning 4%. You also want to find the monthly payment that makes an ordinary annuity have a future value in 4 years of $25,000 when it earns 12%.
Ordinary annuity
The future value of an ordinary annuity having payments P made n times per year for t years earning interest rate r is ...
FV = P((1+r/n)^(nt) -1)/(r/n)
1.
You want the future value for P=1100, r=0.04, n=1, t=5. Using these values in the formula gives ...
FV = $1100(1.04^5 -1)/0.04 = $5957.95
The future value is $5957.95.
2.
You want the payment that makes the future value be 25000 with r=0.12, n=12, t=4.
25000 = P((1 +0.12/12)^(12·4) -1)/(0.12/12) = P(1.612226/0.01) = 61.2226P
Dividing by the coefficient of P gives ...
P = 25000/61.2226 = 408.35
The required monthly payments are $408.35.
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Additional comment
The formula is simple enough to use, but the same calculation can be done by a spreadsheet or an appropriate calculator.
The timing of payments in the second problem is not specified. We have assumed they occur at the end of the month. If they occur at the beginning of the month, they will be the computed amount divided by 1.01 (the monthly multiplier). That would make them $404.30.