You are considering borrowing $10,000 for 3 years at an annual interest rate of 6%. The loan agreement calls for 3 equal payments, to be paid at the end of each of the next 3 years. (Payments include both principal and interest.) The annual payment that will fully pay off (amortize) the loan is closest to:
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A. B. C. D.C
To solve this problem, we need to use the formula for the present value of an annuity:
PV = PMT x (1 - (1 + r)^-n) / r
Where: PV = present value (in this case, the amount of the loan) PMT = payment per period r = interest rate per period n = number of periods
In this case, we know the loan amount is $10,000, the interest rate is 6% per year, and the loan is to be repaid in 3 annual payments.
To find the payment per period (PMT), we can rearrange the formula:
PMT = PV x r / (1 - (1 + r)^-n)
Substituting the known values:
PMT = $10,000 x 0.06 / (1 - (1 + 0.06)^-3) PMT = $10,000 x 0.06 / (1 - 0.8396) PMT = $10,000 x 0.06 / 0.1604 PMT = $600 / 0.1604 PMT = $3,742.65 (rounded to nearest cent)
So the annual payment that will fully pay off the loan is closest to option C: $3,741.
Note that this assumes the payments are made at the end of each year. If the payments were made at the beginning of each year, we would need to use a slightly different formula, but the answer would still be closest to option C.