Question

You have deposited $10,000 in a bank earning interest at 7% p.a. compounded quarterly for four years and five months. At that time, the interest rate changes to 6% p.a. compounded monthly. What is the value of the deposit three years after the change in the rate of interest?

What nominal annual rate compounded quarterly is equivalent to 7.5% p.a. compounded monthly?

You have decided to deposit $500 in the Montreal bank at the end of each quarter for seven years at a rate of 5% p.a. compounded quarterly. How much will be in your account just after you make your last deposit?

Answer 1

1)

Value of the deposits = Initial amount*(1+Annual interest rate/Number of compoundings per year)^*Number of compoundings per year*Number of years)

Value of the deposits = 10000*((1+0.07/4)^(4*4.41666))*((1+0.06/12)^(3*12))

Value of the deposits = $16258.70

2)

Equivalent annual rate = (1+Annual interest rate/Number of compoundings per year)^(Number of compoundings per year)

Equivalent annual rate = ((1+7.5%/12)^12)-1

Equivalent annual rate = 7.763%

7.693% +1 = (1+Annual interest rate compounded quarterly/4)^(4)

Annual interest rate compounded quarterly = 7.480%

3)

Using a financial calculator

PV = 0

PMT = 500

N = 28 (7years*4 contributions per year = 28periods)

I/Y = 5/4 (5%/4 = 1.25% rate per quarterly period)

cpt FV, we get FV = 16639.69

Hence, last deposit $16639.69 is accumulated