Answer:
Explanation:
we need to sovle for the time in an ordinary annuity.
The loan (present value of the annuity) is 12,000
the payment are 1,200 per year
and the rate is 10.10% we need to solve for years:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C $ 1,500
time n
rate 10.10% = 10.10/100 = 0.101
PV $ 12,000
[tex]1500 \times \frac{1-(1+0.101)^{-n} }{0.101} = 12000\\[/tex]
we plug the values and work-out the equation
[tex](1+0.101)^{-n}= 1-\frac{12000\times0.101}{1500}[/tex]
Solve for the right side, and apply logarithmics properties:
[tex](1+0.101)^{-n}= 0.192\\[/tex]
[tex]-n= \frac{log0.192}{log(1+0.101)[/tex]
-n = -17.15110682
n = 17.15
the loan will take 17 years to repay if Mary does annual payment of 1,500
