Question

1. Exercise One: Compute the Future Value of 100,000 USD (U.S. Dollars), 10 years from today, if the interest rate is 8.25%, assuming: (a) simple interest, (b) daily compounding, (c) continuous compounding. Exercise Two: Compute the Future Value of 5,000 USD (U.s. Dollars), 20 years from today, if the interest rate is 6.25%, assuming: (a) simple interest, (b) quarterly compounding, (c) continuous compounding. 2. 3. Exercise Three: Compute the Present Value of 30,000 USD (U.S. Dollars), received 15 vears from today, if the interest rate is 7.45%, assuming: (a) simple interest, (b) daily compounding, (c) continuous compounding. Exercise Four: Compute the Present Value of 25,000,000 USD (U.S. Dollars), received 35 years from today, if the interest rate is 7.25%, assuming: (a) simple interest, (b) monthly compounding, (c) continuous compounding. 4. Exercise Five: The target future value of an investment is $800,000, and its present value is $250,000. Assuming an average interest rate of 4.25%, find the investment horizon under, (a) quarterly compounding, (b) daily compounding. 5. ir

Answer 1

In order to solve the following questions we will need the following 3 formula

A. Simple interest :- A = P + (P*R*T)/100 ...where A is amount, P is principal, R is rate of interest and T is the number of years.

B. Compound interest :- .... where n is the type of compounding (if yearly then n=1, if half-yearly then n=2 if quarterly then n= 4 if daily the n = 365 ) and t is the number of years.

"A = P * (1+-)nt

C. continuous Compounding :-

APet

Hence solving for all questions.

1.a. A = 100000 + (100000*8.25*10/100) = 182,500 USD

1.b. A = 100000 *(1+ 0.0825/365)^(365*10) = 228,166.81 USD

1.c. A = 100000*e^(.0825*10) = 228,188.08 USD

2.a.  A = 5000 + (5000*6.25*20/100) = 11,250 USD

2.b.  A = 5000*(1+ 0.0625/4)^(4*20) =17,283.86 USD

2.c. A = 5000*e^(.0625*20) = 17,451.71 USD

3.a. 30000 = P + (P*7.45*15/100)

i.e. P = 30000 - 111.75P/100

therefore, P +1.1175P =30000

2.1175P =30000

P = 14,167.65 USD

3.b. 30000 = P *(1+ 0.0745/365)^(365*15)

therefore P = 30000 / (1+ .0745/365)^(365*15)

P = 9,814.01 USD

3.c. 30000 = P*e^(.0745*15)

P = 30000/ e^(.0745*15)

P = 9,812.90 USD

4.a. 25000 = P + (P*7.25*35/100)

i.e. P = 25000 - 111.75P/100

therefore, P +2.5375P =30000

3.5375P =25000

P = 7,067.14 USD

4.b. 25000 = P *(1+ 0.0725/12)^(12*35)

therefore P = 25000 / (1+ .0725/12)^(12*35)

P = 1,991.74 USD

4.c. 25000 = P*e^(.0725*35)

P = 25000/ e^(.0725*35)

P = 1,976.60 USD