Question

Question 3. (a) A family member is thinking about funding his granddaughter’s university education in 8 years when she is expected to enrol at UWI, St. Augustine. He opens a special savings account, where he can receive a lump sum in 8 years. If he is desirous of receiving $60,000 in 8 years when his granddaughter is matriculating, how much would you advise him to deposit in the savings account monthly if annual interest rate is 6%? Show all working.

(b) As a prospective home-owner, you have researched the housing market and you are attracted by two offers. Two $380,000 real estate properties with two different Mortgage (amortization) schedules.

Schedule A requires a down payment of 10% while Schedule B requires a down payment of 12%. If the mortgage is over a period of 20 years at an annual mortgage rate of 7%, what would be the monthly repayment amount for both schedules? Assume that the monthly repayment starts 1 month after the mortgage contract is signed and the down payment made. Show all calculations.

Answer 1

3(a):

Initial amount or principal to be invested = A / (1+r)^n = 60000 / (1+0.06)^6 = 42,297.63

where A = amount required / Future value, r = Rate of interest , n - No of years

3(b):

Schedule A, Monthly payment = (P x r) / [1 - (1 / (1 + r)^n] = (342000 x 0.005833) / [1 - (1.005833)^240] = 2,651.44

where, P = Principal loan amount = 380,000 x 90% = 342,000 , r= interest rate per period = .07/12 = 0.005833, n = no of installments = 20x12 = 240

Now, Schedule B, Monthly payment = (P x r) / [1 - (1 / (1 + r)^n] = (334400 x 0.005833) / [1 - (1.005833)^240] = 2,592.52

where, P = Principal loan amount = 380,000 x 88% = 334,400