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

Problem 4

a)

Present value of deposit=PV=$4000

Nominal Rate of interest=r=15%

Number of compounding periods in a year=c=1 (annual compounding)

Nominal interest rate per compounding period=i=r/c=15%/1=15%

Total number of compounding periods=n=number of years*c=4*1=4

FV=PV*(1+i)ⁿ=4000*(1+15%)⁴=$6996.03

b)

Present value of deposit=PV=$4000

Nominal Rate of interest=r=15%

Number of compounding periods in a year=c=2 (semi annual compounding)

Nominal interest rate per compounding period=i=r/c=15%/2=7.5%

Total number of compounding periods=n=number of years*c=4*2=8

FV=PV*(1+i)ⁿ=4000*(1+7.5%)⁸=$7133.91

c)

Present value of deposit=PV=$4000

Nominal Rate of interest=r=15%

Number of compounding periods in a year=c=4 (quarterly compounding)

Nominal interest rate per compounding period=i=r/c=15%/4=3.75%

Total number of compounding periods=n=number of years*c=4*4=16

FV=PV*(1+i)ⁿ=4000*(1+3.75%)¹⁶=$7208.91

d)

Present value of deposit=PV=$4000

Nominal Rate of interest=r=15%

Number of compounding periods in a year=c=12 (monthly compounding)

Nominal interest rate per compounding period=i=r/c=15%/12=1.25%

Total number of compounding periods=n=number of years*c=4*12=48

FV=PV*(1+i)ⁿ=4000*(1+1.25%)⁴⁸=$7261.42

Problem 5

Purchase value of painting=PV=$1200

Expected future value=FV=$5000

Number of periods=n=5 years

Let the annual return be i. So.

FV=PV*(1+i)ⁿ

5000=1200*(1+i)⁵

4.166667=(1+i)⁵

(1+i)=(4.166667)^1/5

(1+i)=1.330325

i=0.330325 or say 33.03%