Question

8. Herman has agreed to repay a debt by using the following repayment schedule. Starting today, he will make $100 payments at the beginning of each month for the next two-and-a-half years. He will then pay nothing for the next two years. Finally, after four-and-a-half years, he will make $200 payments at the beginning of each month for one year, which will pay off his debt completely. For the first four-and-a-half years, the interest on the debt is 9% compounded monthly. For the final year, the interest is lowered to 8.5 % compounded monthly. Find the size of Herman's debt. Round your answer to the nearest dollar.

Please show the work, thanks!

Answer 1

Step 1: Calculate Present Value of $100 Payment Per Month Today

The present value can be calculated with the use of PV (Present Value) function/formula of EXCEL/Financial Calculator. The function/formula for PV is PV(Rate,Nper,PMT,FV,1) where Rate = Interest Rate, Nper = Period, PMT = Payment, FV = Future Value (if any) and 1 indicates Annuity Due.

Here, Rate = 9%/12, Nper = 2.5*12 = 30, PMT = 100 and FV = 0

Using these values in the above function/formula for PV, we get,

Present Value of $100 Payment Per Month Today = PV(9%/12,30,100,0,1) = $2,697.59

_____

Step 2: Calculate Present Value of $200 Payment Per Month Today

The present value can be calculated with the use of PV (Present Value) function/formula of EXCEL/Financial Calculator. The function/formula for PV is PV(Rate,Nper,PMT,FV,1) where Rate = Interest Rate, Nper = Period, PMT = Payment, FV = Future Value (if any) and 1 indicates Annuity Due.

Here, Rate = 8.5%/12, Nper = 1*12 = 12, PMT = 200 and FV = 0

Using these values in the above function/formula for PV, we get,

Present Value of $200 Payment Per Month at the Beginning of Final Year = PV(8.5%/12,12,200,0,1) = $2,309.30

Present Value of $200 Payment Per Month Today = Present Value of $200 Payment Per Month at the Beginning of Final Year/(1+Interest Rate/12)^(Period) = 2,309.30/(1+9%/12)^(12*4.5) = $1,542.58

_____

Step 3: Calculate Value of Debt

The value of debt is arrived as below:

Value of Debt = Present Value of $100 Payment Per Month Today + Present Value of $200 Payment Per Month Today = 2,697.59 + 1,542.58 = $4,240.17

_____

Notes:

1) There can be a slight difference in final answer on account of rounding off values.