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Answer:
(a) 6 months
Step-by-step explanation:
The formula for figuring the monthly payment on an amortized loan can be used for finding the length of time it takes to pay off the loan.
That formula is ...
A = P(r/12)/(1 -(1 +r/12)^(-12t))
where A is the monthly payment, P is the principal value of the loan, r is the annual interest rate, and t is the number of years.
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Using the given information, we can solve for t:
300 = 1568(0.113/12)/(1 -(1 +0.113/12)^(-12t))
1 -(1 +0.113/12)^(-12t) = 1568(0.113)/(12(300))
(1 +0.113/12)^(-12t) = 1 -(1568·0.113)/(12·300) ≈ 0.950782
Taking logs, we get ...
-12t·log(1 +0.113/12) = log(0.950782)
t = log(0.950782)/(-12·log(1 +0.113/12)) ≈ 0.448739 . . . . years
This fraction of a year is ...
(12 months/year)(0.448739 years) = 5.38 months
It will take you 6 months to pay off the loan.