Question

FUTURE VALUE -

(a) How much money would you have in a year if you put $1,000 in the bank at an annual interest rate of 3 percent? How much would you have if you left all of that money in the bank for another year and annual interest rates increased to 4 percent in the second year? (PLEASE INCLUDE FORMULAS UTILIZED TO SOLVE PROBLEM)

(b) How much money would you have in a year if you put $2,500 in the bank at an annual interest rate of 4 percent? How much would you have if you left all of that money in the bank for another year and annual interest rates increased at 5 percent in the second year? (PLEASE INCLUDE FORMULAS UTILIZED TO SOLVE PROBLEM)

PRESENT VALUE OF A LOAN

(c) How much would you loan your brother-in-law if he said he could repay you $100 in six months, $200 in a year, and $500 in two years if you can get 2 percent interest from the bank on a six month CD? Show that you are in fact indifferent between the loan and putting your money in the bank for the next two years. (PLEASE INCLUDE FORMULAS UTILIZED TO SOLVE PROBLEM)

(d) How much would you loan your nephew if he said he could repay you $300 in six months, $400 in a year, and $600 in two years if you can get 3 percent interest from the bank on a six month CD? Show that you are in fact indifferent between the loan and putting your money in the bank for the next two years. (PLEASE INCLUDE FORMULAS UTILIZED TO SOLVE PROBLEM)

Answer 1

a). Future Value = Principal *(1+r)^n,   Here r is interest rate and n is time period
Principal = $1000
Interest rate = 3% per annum
Amount at end of 1 year = 1000*(1+0.03)^1 = $1030
If money stays invested for 2 nd year and interest rate is 4% then amount at the end of 2nd year is:
= 1030*(1+0.04)^1 = $1071.20

b). Principal = $2500
Interest rate = 4% per annum
Amount at end of 1 year = 2500*(1+0.04)^1 = $2600
If money stays invested for 2 nd year and interest rate is 5% then amount at the end of 2nd year is:
= 2600*(1+0.05)^1 = $2730

c). Loan amount would be present values of all the future receipts:
Interest rate = 2% for 6 months
Receipts = $100 in 6 months , $200 in 1 year and $500 in 2 year.
Present Value = Principal / (1+r)^n,    Here r is rate and n is time period.
Loan Amount = 100/(1+0.02)^1 + 200/(1+0.02)^2 + 500/(1+0.02)^4
= (100/1.02) + (200/1.0404) + (500/1.0824) = 98.04 + 192.23 + 461.94 = $752.21 i.e loan amount.
Here some difference is possible for approximation, you can use excel for exact figures.

d).Interest rate = 3% for 6 months
Receipts = $300 in 6 months , $400 in 1 year and $600 in 2 year.
Present Value = Principal / (1+r)^n,    Here r is rate and n is time period.
Loan Amount = 300/(1+0.03)^1 + 400/(1+0.03)^2 + 600/(1+0.03)^4
= (300/1.03) + (400/1.0609) + (600/1.1255) = 291.26 + 377.04 + 533.10 = $1201.4 i.e loan amount.
Here some difference is possible for approximation, you can use excel for exact figures.

In answers c and d formula used is of compounding effect.