Question

Question 1) You invest $100,000 today in an online savings account for 5 years. If the interest rate is 4% p.a., calculate the future value under each of the following scenarios:

a) Interest rates are compounded annually
b) interest rates are compounded monthly

Question 2) You expect to receive $50,000 from your superannuation in 3 years from today. If the interest rate is 8% p.a., calculate the future value under each of the following scenarios:

a) interest rates are compounded annually
b) interest rates are compounded quarterly

Answer 1

question 1:

a. amount invested (present value) = 100,000
Amount after 5 years (future value)=?

Formula:
Future value= present value (1+r)^n
r =interest rate (0.04 or 4%)
n = number of periods (5)

FV = 100,000(1+0.04)^5

FV= $121,665.29 (amount available at year 5).

b. amount invested (present value) = 100,000
Amount after 5 years (future value)=?

Formula:
Future value= present value (1+r)^n
r =interest rate (0.04/12)=0.00333
n = number of periods (5 x 12=60)

FV = 100,000(1+0.0033333)^60

FV= $122,099.66 (amount available at year 5).

Question 2:

Formula:

Present value = future value/(1+effective interest rate)^number of periods.

a. Future value is $50,000

Effective interest rate is 8%

Present value = 50,000/(1.08)^3

The present value is $39,691.61

b. Future value is $50,000

Effective interest rate is {8%/12}= 0.66667% or 0.0066667per month

Number of periods is 36 months.

Present value = 50,000/(1.0066667)^(36)

The present value is 39,362.73