Question

You want to buy a car which will cost you $10,000. You do not have sufficient funds to purchase the car. You do not expect the price of the car to change in the foreseeable future. You can either save money or borrow money to buy the car.

• Plan 1: You decide to open a bank account and start saving money. You will purchase the car when you have sufficient savings. The nominal interest rate for the bank account is 6% per annum compounded monthly.

a) You will make regular deposits in your bank account at the start of each month for the next 2.5 years. Calculate the minimum required monthly savings to be deposited into the bank such that you would have sufficient funds to purchase the car in 2.5 years. (1 mark)

Answer 1

Future Value of an Annuity Due (Beginning of the month payment)

Future Value = $1,0000

Monthly interest rate (r) = 0.50% per month [6.00% / 12 Months]

Number of years (n) = 30 Years [2.50 Years x 12 Months]

Monthly Deposit amount (P) = ?

Therefore, Future Value of an Annuity Due = (1 + r) x P x [{(1+ r)ⁿ - 1} / r ]

$10,000 = (1 + 0.0050) x P x [{(1 + 0.0050)³⁰ - 1} / 0.0050]

$10,000 = 1.0050 x P x [(1.161400083 – 1) / 0.0050]

$10,000 = 1.0050 x P x [0.161400083 / 0.0050]

$10,000 = P x 32.44141666

P = $10,000 / 32.44141666

P = $308.25 per month

Hence, the monthly deposit amount will be $308.25