Question

An amount was deposited into an account paying interest of 14% per annum effective for 22 months compounded monthly. At the end of the period the account was worth R20 000. What was the amount deposited?

Answer 1

To find the amount deposited, we can use the formula for compound interest:

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

Where:
A = the amount in the account at the end of the period (R20 000)
P = the principal amount (the amount deposited)
r = annual interest rate (14% or 0.14)
n = number of times the interest is compounded per year (12 since it is compounded monthly)
t = time the money is invested for (22/12 years)

Substitute the given values into the formula:

20,000 = P(1 + 0.14/12)^(12*(22/12))

20,000 = P(1 + 0.01166666667)^22

20,000 = P(1.01166666667)^22

20,000 = P(1.282159)

Divide both sides by 1.282159:

P = 20,000 / 1.282159

P ≈ R15,581.53

Therefore, the amount deposited was approximately R15,581.53.