Question

Some debts can be repaid at a discount if they are paid early. Jen borrowed money...

Some debts can be repaid at a discount if they are paid early. Jen borrowed money 5 years ago and the loan is due 2 years from now. If she pays it back in 2 years, the debt will be $10 346. If she repays it now, she can get a discount of 8% , compounded semi-annually.

a) How much will she have to pay now?

b) How much will she save if she pays early?

Math   Algebra   
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Answer #1

Let Jen pay $ X now to settle the debt now which is payable after 2 years.

The formula for future value (F) of an amount (X), after n years, where interest rate is r % and interest is compounded t times per year is F = X(1+r/100t)nt. Here, F = $ 10346, n = 2, r = 8 = 0.08 and t = 2. Therefore, X(1+0.04)2*2 = 10346 or, X* 1.16985856 = 10346. Hence, X = 10346/1.16985856 = 8843.80( on rounding off to 2 decimal places).

a). Thus, Jen will have to pay $ 8843.80 now to settle the debt.

b). Jen will save $ 10346 -$8843.80 = $ 1502.20, if she pays early.

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