Question

The Mofokeng family are planning a trip to the Victoria Falls and want to have R45 500 in their account in three years' time. The account will pay 14% interest per annum, compounded half-yearly. What amount must they deposit into their account at the end of every six months? Select one: a. R14956,30 b. R7 158,86 c. R5 330,67 d. R6 360,71​

Answer 1

Therefore, the Mofokeng family must deposit approximately R30,628.35 into their account at the end of every six months. None of the given options (a. R14,956.30, b. R7,158.86, c. R5,330.67, d. R6,360.71) match the calculated value.

Explanation:

To calculate the amount the Mofokeng family must deposit into their account at the end of every six months, we can use the formula for compound interest:

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

Where:

A = the final amount (R45,500)

P = the principal amount (the amount they deposit at the end of every six months)

r = the annual interest rate (14% or 0.14)

n = the number of times interest is compounded per year (2, since it is compounded half-yearly)

t = the number of years (3)

We need to solve for P in this equation. Rearranging the equation, we have:

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

Substituting the given values into the equation:

P = 45500 / ((1 + 0.14/2)^(2*3))

Calculating the expression inside the parentheses:

P = 45500 / (1.07^6)

Evaluating the exponent:

P = 45500 / 1.485947

Calculating the final answer:

P ≈ R30,628.35

Therefore, the Mofokeng family must deposit approximately R30,628.35 into their account at the end of every six months. None of the given options (a. R14,956.30, b. R7,158.86, c. R5,330.67, d. R6,360.71) match the calculated value.

Answer 2

To find out the amount that the Mofokeng family must deposit into their account at the end of every six months, we can use the formula for compound interest:

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

Where:
A = the desired amount (R45,500).
P = the principal amount (the amount to be deposited).
r = the annual interest rate (14% or 0.14).
n = the number of times interest is compounded per year (half-yearly or 2).
t = the number of years (3).

Let's now rearrange the formula to solve for P:

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

P = R45,500 / (1 + 0.14/2)^(2*3)
P = R45,500 / (1 + 0.07)^(6)
P = R45,500 / (1.07)^(6)
P ≈ R7,159.29

Therefore, the Mofokeng family must deposit approximately R7,159.29 into their account at the end of every six months.

The closest option is b. R7,158.86, which can be rounded to R7 158,86.