How much would you have to invest today to receive the following? a. $15,500 in
ID: 2616430 • Letter: H
Question
How much would you have to invest today to receive the following? a. $15,500 in 12 years at 11 percent. (Do not round intermediate calculations. Round your final answer to 2 decimal places.) b. $20,000 in 19 years at 7 percent. (Do not round intermediate calculations. Round your final answer to 2 decimal places.) c. $8,100 each year for 18 years at 15 percent. (Do not round intermediate calculations. Round your final answer to 2 decimal places.) d. $56,000 each year for 25 years at 8 percent. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)
Explanation / Answer
a.We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.
15500=P(1.11)^12
P=$15500/(1.11)^12
=$15500*0.285840823
=$4430.53(Approx).
2.
We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.
20000=P(1.07)^19
P=$20000/(1.07)^19
=$20000*0.276508333
=$5530.17(Approx).
3.
Present value of annuity=Annuity[1-(1+interest rate)^-time period]/rate
=$8100[1-(1.15)^-18]/0.15
=$8100*6.127965874
=$49636.52(Approx).
4.
Present value of annuity=$56000[1-(1.08)^-25]/0.08
=$56000*10.67477619
=$597787.47(Approx).
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