A twenty-year note for $1000.00 bearing interest at 9% compounded monthly is discounted at 5% compounded quarterly four years and six months before maturity. Find the proceeds of the note.
A) $6009.15
B) $4805.10
C) $133.07
D) $4800.65
E) $4741.93

Question

Quizplus · Accepted Answer

To solve this problem, we need to use the formula for present value of a loan:

PV = C[(1 - (1 + r/n)^(-nt))/(r/n)]

where PV is the present value, C is the principal or face value of the loan, r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the number of years.

First, we need to find the value of the loan four years and six months before maturity, which is 15.5 years. To do this, we can use the formula:

PV = FV/(1 + r/n)^nt

where FV is the future value of the loan at maturity. From the given information, we know that:

FV = $1000(1 + 0.09/12)^(12*20) = $7328.63

So, the present value four years and six months before maturity is:

PV = $7328.63/(1 + 0.05/4)^(4*15.5/12) = $4805.10

Therefore, the answer is B, $4805.10.

A Twenty-Year Note for $1000