Bonita invest R 36 000 into a fixed deposit account, which offers her an interest rate of 12%. The interest…

Question

Bonita invest R 36 000 into a fixed deposit account, which offers her an interest rate of 12%. The interest is compound.

ScanSolve AI Tutor · Accepted Answer

To calculate the future value of Bonita's investment for each compounding period, we use the compound interest formula:

A = P\left(1 + \frac{r}{n}\right)^{nt}

Where:
$A$ = future value of the investment
$P$ = principal amount (R26 000)
$r$ = annual interest rate (12% or 0.12)
$n$ = number of times interest is compounded per year
$t$ = number of years

Since the time period is not specified, we will assume $t = 1$ year for all calculations.

Calculate the future value for Annually compounded interest.
For annually compounding, $n = 1$ .
$A = 26000\left(1 + \frac{0.12}{1}\right)^{1 \times 1}$ $A = 26000(1 + 0.12)^1$ $A = 26000(1.12)$ $A = \text{R}29120.00$
Calculate the future value for Monthly compounded interest.
For monthly compounding, $n = 12$ .
$A = 26000\left(1 + \frac{0.12}{12}\right)^{12 \times 1}$ $A = 26000(1 + 0.01)^{12}$ $A = 26000(1.01)^{12}$ $A \approx 26000 \times 1.12682503$ $A \approx \text{R}29300.05$
Calculate the future value for Half-yearly compounded interest.
For half-yearly compounding, $n = 2$ .
$A = 26000\left(1 + \frac{0.12}{2}\right)^{2 \times 1}$ $A = 26000(1 + 0.06)^2$ $A = 26000(1.06)^2$ $A = 26000(1.1236)$ $A = \text{R}29213.60$
Calculate the future value for Quarterly compounded interest.
For quarterly compounding, $n = 4$ .
$A = 26000\left(1 + \frac{0.12}{4}\right)^{4 \times 1}$ $A = 26000(1 + 0.03)^4$ $A = 26000(1.03)^4$ $A \approx 26000 \times 1.12550881$ $A \approx \text{R}29263.23$
The future values after 1 year for each compounding period are:
1. Annually: $\boxed{\text{R}29120.00}$
2. Monthly: $\boxed{\text{R}29300.05}$
3. Half-yearly: $\boxed{\text{R}29213.60}$
4. Quarterly: $\boxed{\text{R}29263.23}$

Bonita invest R 36 000 into a fixed deposit account, which offers her an interest rate of 12%. The interest is compound.

Step-by-step solution

Calculate the future value for Annually compounded interest.

Calculate the future value for Monthly compounded interest.

Calculate the future value for Half-yearly compounded interest.

Calculate the future value for Quarterly compounded interest.

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