Question

a. Given: Mr. Uga has $100 million to invest. He wants his investment to triple in 6 years. A bank offers him an attractive rate of return that is compounded monthly. Solve for: What interest rate per month should the bank pay Mr. Uga in order for his investment to triple in 6 years? b. Given: Mr. Buga would like to invest a lump sum of money today in order withdraw $10,00 five years from today, $10,000 ten years from today, and $10,000 twenty years from today. A bank offers to pay him 12%/year compounded monthly for his investment. Following is a cash flow diagram representation of the problem: $10,000 $10,000 $10,000 على تلك 1 2 4 5 9 10 19 20 P = ? Solve for: How much money should Mr. Buga deposit into the bank today in order to withdraw $10,000 at the end of the 5th year, $10,000 at the end of the 10th year, $10,000 at the end of the 20th year.

Answer 1

a)

Present value of deposit=PV=$100 millions

Future value of deposit=FV=3*100 =$300 millions

Interest rate per month=i=?

Number of periods=6*12=72 months

We know that

FV=PV*(1+i)^n

300=100*(1+i)^72

3=(1+i)^72

or

i=3^(1/72)-1=1.5376% per month

b)

Monthly interest rate=i=12%/12=1%

PV of deposit=PV of $10000 to be received after 5 years+PV of $10000 to be received after 10 years+PV of $10000 to be received after 20 years

P=10000*(P/F,0.01,60)+10000*(P/F,0.01,120)+10000*(P/F,0.01,240)

Let us calculate the interest factors

(P/F,0.01,60)=1/(1+0.01)^60=0.55044962

(P/F,0.01,120)=1/(1+0.01)^120=0.30299478

(P/F,0.01,240)=1/(1+0.01)^240=0.09180584

So,

P=10000*0.55044962+10000*0.30299478+10000*0.09180584=$9452.50