Ajax plc just decided to save £1,500 a month for the next ﬁve years as a safety net for recessionary periods.The money will be set aside in a separate savings account which pays 3.25% interest compounded monthly.It deposits the ﬁrst £1,500 today.If the company had wanted to deposit an equivalent lump sum today, how much would it have had to deposit?

Question

Quizplus · Accepted Answer

Using the formula for compound interest:

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

Where:

A = amount after time t
P = principal (initial amount)
r = annual interest rate as a decimal
n = number of times the interest is compounded per year
t = time in years

We can solve for the principal (P) in the scenario where the company has already deposited £1,500 and wants to know how much they would have had to deposit in a lump sum today.

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

A = amount after 5 years = £90,000 (since they are saving £1,500 per month for 60 months)
r = 3.25% per year = 0.0325
n = 12 (since interest is compounded monthly)
t = 5 years

£90,000 = P(1 + (0.0325/12))^(12*5)
£90,000 = P(1.003081)^60
£90,000 = P(1.219497)
P = £90,000/1.219497
P = £73,862.98

However, they have already deposited £1,500 today, so the lump sum they would have had to deposit today is:

£73,862.98 + £1,500 = £83,362.98

This is closest to option B (£83,189.29).

Ajax Plc Just Decided to Save £1,500 a Month for the Next