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.)

Answer 1

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).