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zalisa [80]
3 years ago
11

Use the formula for the present value of an ordinary annuity or the amortization formula to solve the following problem. PV=​$20

,000​; i=0.01​; PMT=​$250​; n=​? n=(round up to the nearest integer)
Mathematics
1 answer:
White raven [17]3 years ago
8 0
Assuming monthly payment of $250, which implies APR=0.01*12=0.12.
If it is different, please specify.

target P=20000,
A=250
n=to be determined such that P>=target P=20000
The annuity equation with given (monthly) payment is given by
P=250(P/A,i,n)
=A((1+i)^n-1)/(i(1+i)^n)
=250(1.01^n-1)/(0.01(1.01)^n)
=25000(1.01^n-1)/(1.01^n)
Solve for n by trial and error,
Rewrite 
20000<=25000(1-1/1.01^n)
=>
1.01^n>=25000/20000=1.25
Take log on both sides,
n*log(1.01)>=log(5)
n>=log(5)/log(1.01)=161. 75
=> n=162 (next integer)
Check:
P=250(P/A,0.01,162)=250*(1.01^162-1)/(.01*1.01^162)=20012.56 ok.
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