Question

1a) Lucy invested $950 five years ago. Her investment paid 7.2% interest compounded monthly. Lucy's twin sister Laurie invested $900 at the same time. But Laurie's investment earned 8% interest compounded quarterly. How much is each investment worth today?

1b) Carl is considering the purchase of an investment that will pay him $12,500 in 12 years. If Carl wants to earn a return equal to 7% per year (annual compounding), what is the minimum amount he should be willing to pay for the investment today?

Answer 1

a.

Lucy:

We use the formula:
A=P(1+r/1200)^12n
where
A=future value
P=present value
r=rate of interest
n=time period.

Hence

A=$950(1+0.072/12)^(12*5)

=$950*1.431788412

=$1360.20(Approx).

Laurie:

We use the formula:
A=P(1+r/400)^4n
where
A=future value
P=present value
r=rate of interest
n=time period.

Hence

A=$900(1+0.08/4)^(4*5)

=$900*1.485947396

=$1337.35(Approx).

b.

Present value of inflows=cash inflow*Present value of discounting factor(rate%,time period)

=$12500/1.07^12

=$12500*0.444011959

which is equal to

=$5550.15(Approx).