Question

4) Determine the value at the end of four years of
a $5,000 investment today that pays a nominal annual interest rate of 15%, compounded:

a)

Annually

b)

Semiannually

c)

Quarterly

d)

Monthly

5. You are considering buying a painting by a local
artist for $1,200. You believe that this artist is just
about to be discovered, and think that five years from now the painting will be worth $5,000. If you are
correct, what average annual return would you earn on this investment over this period?

Answer 1

Solution:-

a). We use the formula,

A=P (1+r/2) ^2n
where
A=future value
P=present value
r=rate of interest
n=time period.

A=$5000(1+0.15/2) ^ (2*4)

=$5000 * 1.78347783

=$8917.39 (Approx.)

b).We use the formula
A=P (1+r/4) ^ 4n

A=$5000(1+0.15/4) ^ (4*4)

=$5000*1.80222

=$9011.14(Approx.)

C). We use the formula:
A=P(1+r/1200)^12n

A=$5000(1+0.15/12) ^ (12*4)

=$5000*1.815355

=$9076.8 (Approx.).

5). FV=PV*(1+i) ^n

FV=future value=5000

PV=present value=1200

i=average annual return =?

n=5

5000=1200*(1+i) ^5

1+I = (5000/1200)^(1/5)

i=1.330325-1

i=0.330325

i=33.0325%

The average annual return is 33.03%