Question

1. Austin is planning to purchase a new car in exactly 4 years and anticipates the cost will equal $30,000. He expects to receive a bonus cheque from his employer this year and wants to deposit sufficient funds into his bank account one year from today so that he has enough savings to purchase his car. Assuming his savings account earns 5% per year, how much must Austin deposit into his account?

2. Susan is planning for retirement, which she anticipates will occur in 20 years. She currently has $100,000 in savings in her Registered Retirement Savings Plan (RRSP). Her objective is to have $500,000 in her RRSP when she retires. Assuming she makes no additional deposits into her RRSP, what annual rate of return must Susan earn to achieve her objective?

Answer 1

Q-1)

Future avlue to accumulate in 4 years = $30,000

Austin will deposit enough amount in bank 1 year from now such that deposit along with interest accumulate the future value.

As the deposit will take place 1 year from now, we will calculate the Present Value at year 1:-

Where,

r = Interest rate = 5%

n= no of periods = 3 years ( from year 4 to year 1)

PV1 = $25,915.13

So, amount Austin deposit into his account 1 year from now os $25,915.13

Q-2)

Present Value of amount available for Investment = $100,000

Future Value of amount to be accumulated = $500,000

Calculating the Annual rate of Interest that would be earned to accumulated the amount:-

Where,

r = Interest rate

n= no of periods = 20 years

m = no of times compounding in a year = 1 (compounded annually)

taking 20-root on both sides,

1.083798 = (1+r)

r = 8.3798%

So, annual rate of return must Susan earn to achieve her objective is 8.38%