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I have a complicated math problem?
say a person borrows $40,000 at 15% interest. This isn't simple interest. It's the other type compound. The person makes $800 a month payments. How long should it take to completely pay off the loan?
2 Answers
- billrussell42Lv 77 years agoFavorite Answer
"other type compound" ? monthly? daily? continuously? I'll assume monthly
Mortgage payment
A = Pr(1+r)ⁿ / ((1+r)ⁿ–1)
A is the periodic amortization payment
P is the principal amount borrowed
r is the percentage rate per period; for a monthly payment,
take the Annual Percentage Rate (APR)/12
n is the number of payments; for monthly payments over 30 years,
12 months x 30 years = 360 payments.
r = 0.15/12 = 0.0125
800 = (40000)(0.0125)(1.0125)ⁿ / ((1.0125)ⁿ–1)
solve for n
(1.0125)ⁿ / ((1.0125)ⁿ–1) = 1.6
(1.0125)ⁿ = 1.6((1.0125)ⁿ–1)
(1.0125)ⁿ = 1.6(1.0125)ⁿ – 1.6
(1.0125)ⁿ (1 – 1.6) = – 1.6
(0.6)(1.0125)ⁿ = 1.6
(1.0125)ⁿ = 2.666667
log both sides
n log (1.0125) = log 2.666667 = 0.4259687
n = 0.4259687 / 0.005395 = 79 months
- M3Lv 77 years ago
assuming compounding is also monthly@1.25% (usual practice)
the formula is n = -ln(1-PVr/PMT)/ln(1+r) = - ln(1-40,000*0.0125/800)/ln(1.0125)
= 78.96 mths
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