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)

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

c) You will make regular deposits of $2,000 at the end of each year. Calculate how long will it take for you to have sufficient funds to purchase the car. (1 mark)

Answer 1

a)Future value of the car (FV )= $ 10000

Rate of interest monthly (rate) = 6/12 = 0.5%

Time period (nper) = 2.5 *12 = 30 months

Present value (PV) =0

We have to find the payment required (PMT ) for each month

Using the PMT function in excel ,

=PMT( rate, nper, PV,- FV)

=PMT( 0.5% , 30, 0, -10000)

= $ 309.79 (Answer)

b) Considering that there are 52 weeks in a year

Rate of interest weekly (rate ) = 6%/52 = 0.1154%

Time (nper) = 52*2.5 = 130 weeks

Using the PMT function in excel ,

=PMT( rate, nper, PV,- FV)

=PMT( 0.1154% , 130, 0, -10000)

= $ 71.34 (Answer)

c) Given ,

PMT = $ 2000

PV= 0

FV= 10000

rate = 6%

We need to find nper,

=nper(rate,pmt,pv,fv)

=nper(6%,-2000,0,10000)

=4.5 years (answer)