Question

Alexis want to buy a house in 5 years. She wants to save $75,000 over the next five years for a down payment. If she can earn an annual rate of 9% on her savings, how much must she deposit in equal payments at the end of each month for the next five years to reach her goal?

A) $1,250                    B) $765.87                  C) $994.38                  D) $8,420.13

Alexis is ready to buy her house. She will purchase the $450,000 house with her $75,000 down payment and finance the rest with a 20 year, 6% annual rate mortgage with equal end of month payments. What will be her monthly payment?

A) $2,134.76               B) $3,223.94               C) $1,701.69               D) $2,686.62

Answer 1

Question 1

Future value of Annuity = A [((1+r)ⁿ-1) / r]

Where

A - Annuity payment = ?

r - rate per period = .09/12 = 0.0075

n - no. of periods = 5*12 = 60

75000 = A* [((1+.0075)^60 -1) / .0075]

= A* [(1.56568102694 -1) / .0075]

= A*(0.56568102694/.0075)

= A*75.4241369253

A = 75000/75.4241369253

= $994.38

Question 2

EMI = [P * I * (1+I)^N]/[(1+I)^N-1]

P =loan amount or Principal = 450000-75000 = 375000

I = Interest rate per month = .06/12 = 0.005
N = the number of installments = 20*12 = 240

EMI = [375000*.005*1.005^240]/[1.005^240-1]

= [375000*.005*3.31020447581]/[3.31020447581-1]

= 6206.63339214/2.31020447581

= $2,686.62