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Wed 29 Sep, 2004 07:59 pm
Stephnaie buys a boat by paying 10% down and by financing the balance with a bank loan at 15%/a, compounded monthly. She arranges to amortize the loan by making monthly payments of $225 each for three years. Determine what Stephanie paid for the boat.
Boat problem
Let At be the total amount for the boat, then Al is the amount of the loan and Al=90%At
The annual compounded interest is 15% paid monthly this is i=15%/1200=0.0125
n is three years paid monthly, so n=12*3=36
There is a neat formulae used for loan amortization it's
P=Ai(1+i)^n/[(1+i)^n-1]
where P is period payment
A is amount borrowed
n is number of payments
i is period interest rate (fractional)
Rearranging to solve for A this becomes
A=P[(1+i)^n-1]/[i(1+i)^n]
putting in P=$225, n=36, i=0.0125 you get A=$10600.31 say $10600
This is the loan amount Al
The total cost of the boat is At=Al/.9 or At=$11778
Rap
ah, the formula was what i was seeking. thank you
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