Question

Q1) Richard wants to save $100,000 in 12 years. He is offered the following three options by his bank:

An account with interest rate 4.5% and annual compounding.

An account with interest rate 4.0% and semi-annual compounding.

An account with interest rate 3.7% and quarterly compounding.

a) Determine how much he must save today to reach his goal in 12 years.

b) Which of the options above would you recommend? Explain your answer.

Answer 1

a)

Annual compounding:

Present value = Future value / (1 + r)^n

Present value = 100,000 / (1 + 0.045)^12

Present value = 100,000 / 1.695881

Present value = 58,966.39

He should save $58,966.39

Semi-annual compounding:

Rate = 4% / 2 = 2%

Number of periods = 12 * 2 = 24

Present value = Future value / (1 + r)^n

Present value = 100,000 / (1 + 0.02)^24

Present value = 100,000 / 1.608437

Present value = $62,172.15

He should invest $62,172.15

Quarterly compounding:

Number of periods = 12 * 4 = 48

Rate = 3.7% / 4 = 0.925%

Present value = Future value / (1 + r)^n

Present value = 100,000 / (1 + 0.00925)^48

Present value = 100,000 / 1.555752

Present value = $64,277.59

He should invest $64,277.59

b)

He should choose the first option as it has the lowest present value.