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Debts of $6800.00 due three months from now and $2600.00 due twenty-one months from now are...

Debts of $6800.00 due three months from now and $2600.00 due twenty-one months from now are to be settled by two equal payments due in three months and nine months from now respectively. Determine the size of the equal replacement payments if interest is 5.5% p.a. compounded quarterly.

Expert Solution

Step 1: Find the Present Value of debts due three months and twenty one months from now

Interest rate = 5.5% per annum or 1.375% per quarter (since it is compounded quarterly)

a. Debt due in 3 months from now or 1 quarter from now = $6,800

Present Value of Debt due in 3 months = $6,800 * Discount factor of 1.375% for 3 months or 1 quarter

=$6,800*(1/(1+1.375%)^1) = $6,800*0.98644 = $6,707.79

b. Debt due in 21 months from now or 7 quarters (21/3) from now = $2,600

Present Value of Debt due in 21 months = $2,600 * Discount factor of 1.375% for 21 months or 7 quarters

=$2,600*(1/(1+1.375%)^7) = $2,600*0.90883 = $2,362.96

c. Total Present Value = $6,707.79 + $2,362.96 = $9,070.75

Step 2: Find the Equal payment of Present Value of Total Debt

1st equal payment in 3 months or 1 quarter.

Present Value Factor of payment in 3 months or 1 Quarter from now = (1/(1+1.375%)^1) = 0.98644

2nd equal payment in 9 months or 3 quarters.

Present Value Factor of payment in 9 months or 3 Quarter from now = (1/(1+1.375%)^3) = 0.95986

Total Present Value Factor of two equal payments= 0.98644 + 0.95986 = 1.94630

Equal Payment to be made in 3 months and 9 months from now = Present Value of debt / Total Present Value Factor of two equal payments

= $9,070.75/1.94630 = $4,660.51

Thus, size of the equal replacement payments = $4,660.51

jeff jeffy answered 1 year ago

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