Question

Question 5

You wish to accumulate R197 000 in five years. You deposit a single amount in an account today that pay
12% interest per year, compounded quarterly. The amount that you deposit is equal to?

Answer 1

We can use the formula for compound interest to find the amount that needs to be deposited:

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

where:

A = accumulated amount

P = principal amount (amount to be deposited)

r = annual interest rate (as a decimal)

n = number of times interest is compounded per year

t = time in years

In this case, we have:

A = R197 000

r = 0.12 (12% as a decimal)

n = 4 (quarterly compounding)

t = 5 years

Substituting these values into the formula, we get:

R197 000 = P(1 + 0.12/4)^(4 x 5)

Simplifying:

R197 000 = P(1.03)^20

P = R197 000 / (1.03)^20

P = R94 838.36 (rounded to the nearest cent)

Therefore, the amount that needs to be deposited today is R94 838.36.