Question

Straight bank loan. Left Bank has a standing rate of 8.1 % ?(APR) for all bank loans and requires monthly payments. What is the monthly payment if a loan is for ?(a?) $ 135,000 for 4 ?years, ?(b?) $ 260,000 for 11 ?years, or ?(c?) $ 1,250,000 for 26 ?years? What is the effective annual rate of each of these? loans?

Answer 1

In order to find the monthly payment that we will have to make on the loan taken, we will use the following formula

Let L be the amount borrowed as part of the loan which has to be paid off monthly with value P . Let the term be "n" months and monthly interest be "C"

A

P = L[c(1 + c)ⁿ]/[(1 + c)ⁿ - 1]

c= .081/12 = .00675

n = 4 years and monthly payment , hence 4*12 = 48

P= 135000[ .00675*(1+.00675)^48] / [(1+.00675)^48 -1] = 3302.085

B

Using the same formula above and replacing n with (11*12) =132 | L with 260000

P= 260000[ .00675*(1+.00675)^132] / [(1+.00675)^132 -1] = 2982.03

Option C

P= 1250000[ .00675*(1+.00675)^312] / [(1+.00675)^321 -1] = 9616.35

Effective Annual rate = [(1+ interest rate per period / number of period )^number of period ] -1

EAR = 8.4076