9514 1404 393
Answer:
2.5 years
$736 in interest
Step-by-step explanation:
The relationship between the values in an amortization is ...
A = P(r/12)/(1 -(1 +r/12)^(-12t))
Here, we have A = 140, P = 3400, r = 0.16 and we want to find t
140 = 3400(0.16/12)/(1 -(1 +0.16/12)^(-12t))
1 -(1 +0.16/12)^(-12t) = 1/3.0882353
(1 +0.16/12)^(-12t) = 0.67619048
Taking logarithms gives ...
-12t·log(1 +0.16/12) = log(0.67619048)
t = log(0.67619048)/(-12·log(1+0.16/12)) ≈ 2.46177
It will take about 2.5 years to pay off the loan.
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The total of payments is ...
(2.46177)(12)($140) = $4135.77
so, the interest paid is ...
$4135.77 -3400 = $735.77
You will pay about $736 in interest over the life of the loan.
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<em>Additional comment</em>
The number of payments is calculated to be about 29.54. You would probably make 30 payments, with the last payment being a different amount than $140. The actual amount will depend on when the payment is made, and the amount of it that is finance charge. We believe the remaining balance after 29 payments will be $75. After a full month, the finance charge due on that amount is $1.00, bringing the total amount of interest paid to $736.
If the loan is paid off in the middle of the month, the interest due is reduced. Above, we have calculated interest based on a last payment made part way through the month. We rounded up, partly because of the ambiguity in the final payment.
