Question

debt of $42000 is repaid by making payments of $4500. If interest is 9% compounded monthly, for how long will payments have to be made at the end of every six months?

Answer 1

Solution :-

Amount Financed = $42,000

Semiannual payment = $4,500

Interest Rate per month = 9% / 12 = 0.75%

Semiannual rate = ( 1 + 0.0075 )⁶ - 1 = 0.04585 = 4.585%

Now we need to find n

= $42,000 = $4,500 * PVAF ( 4.585% , n )

= 9.333 = [ 1 - ( 1 + 0.04585 )^-n ] / 0.04585

0.42795 = 1 - ( 1 + 0.04585 )^-n

( 1 + 0.04585 )ⁿ = 1.74811

Take log both sides

n log ( 1.04585 ) = log ( 1.74811 )

n = 0.242567 / 0.01947033

n = 12.45 Semiannual periods

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