Question

Peter wants to save $500,000 to buy a sport car. He plans to make a deposit of $8,000 each month to achieve this goal. ABC Bank offers a deposit rate of 0.5% per month while DEF Bank offers a deposit rate of 6% with quarterly compounding.

1. a) Which bank should Peter choose? Briefly explain your answer with appropriate calculations [within 20 words].

2. b) After making the deposit into the chosen bank as mentioned in part (a), how long does Peter have to wait to achieve his goal if he starts making his first deposit

   1. i) today?

   2. ii) one month later?

   3. iii) six months later?

3. c) ABC bank has poor credit ratings and the management of the bank has recently offered higher saving interest rates to attract and retain new customers. Peter told you that he can

   

5. Penalties for late submission of assignment – 30% of the total marks awarded will be deducted for each day.

  

also formulate a strategy that can achieve his target without using any of his own capital. The strategy is to borrow a 5-year loan of $400,000 from OZ bank with a fixed monthly interest rate of 0.1%, and immediately, he deposits the whole amount into ABC bank saving account to earn an interest rate spread of 0.4% (0.5% - 0.1%). Peter believed that his plan is perfect, risk free and does not need any capital funding at all. He also claimed that he will know exactly how long he has to wait by simply solving the variable “t” in the below equation 1:

Equation 1: $400,000(1 + 0.4%)? = $500,000

1. i) Solve the value of “t” in above equation 1. Do you agree with Peter’s strategy? Briefly explain your answer [within 50 words].

2. ii) Do you agree with Peter’s strategy is really so perfect and has no risk as he think? Briefly explain your answer [within 150 words].

Answer 1

Formula for calculating future value of present investment.

A = P (1+r/n)^n

Where A = Future value of amount

p = initial investment

r = rate of return

n = number of compounds

Option 1 - Investing 8000 at 0.5% per annum or 6% monthly compounding

A = 500000

P=8000

r = 0.06 (6% that 0.5% per month 6/100)

Lets replace the values with formula

500000 = 8000 ( 1+0.06/12)^12

500000=8000 (1.06/12)^12

50000 = 8000 ( 0.088333 ) ^ 12

50000 = 8493.422

No of period required to invest = 500000/8493.422

= 58.86908 months. peter need to invest in ABC bank to accumulate 500000

Lets analyse the 6% quarterly compounding and replace value

500000 = 8000 ( 1+0.06/4) ^ 4 ( number of quarters in a year is 4 )

The product will be as solved above is 58.88651 months.

Therefore if he invests in ABC back he will be gaining more than DEF bank