Lihle needs 4800 for her refugees at the university of fort hare.She applies for a loan at two different banks A.Capitec offers 12% simple interest p.a to be paid in 3 years B.ABSA offers 7,5% p.a compound interest to be paid in 3 years Calculate her options and advise which option she should take

Principal amount: $P = \mathrm{R}4800$

Option A: Capitec (12% simple interest p.a., 3 years)

Step 1: Simple interest formula

$$I = P \times r \times t$$

Substitute $P = 4800$, $r = 0.12$, $t = 3$:

$$I = 4800 \times 0.12 \times 3$$ $$4800 \times 0.12 = 576$$ $$576 \times 3 = 1728$$

$I = \mathrm{R}1728$

Step 2: Total repayment

$$A_A = P + I$$ $$A_A = 4800 + 1728 = 6528$$

$A_A = \mathrm{R}6528$
Alternatively:

$$A_A = P(1 + rt) = 4800(1 + 0.12 \times 3)$$ $$1 + 0.36 = 1.36$$ $$4800 \times 1.36 = 6528$$

Option B: ABSA (7.5% compound interest p.a., 3 years)

Step 1: Compound amount formula (annually compounded)

$$A_B = P(1 + r)^n$$

$r = 0.075$, $n = 3$:

$$A_B = 4800 \times (1.075)^3$$

Step 2: Compute $(1.075)^2$

$$1.075 \times 1.075$$ $$1.075 \times 1 = 1.075$$ $$1.075 \times 0.075 = 0.080625$$ $$1.075 + 0.080625 = 1.155625$$

$(1.075)^2 = 1.155625$

Step 3: Compute $(1.075)^3 = 1.155625 \times 1.075$

$$1.155625 \times 1 = 1.155625$$ $$1.155625 \times 0.07 = 0.08089375$$ $$1.155625 \times 0.005 = 0.005778125$$ $$1.155625 + 0.08089375 + 0.005778125 = 1.242296875$$

Step 4: Total repayment

$$A_B = 4800 \times 1.242296875$$ $$4800 \times 1 = 4800$$ $$4800 \times 0.242296875$$ $$4800 \times 0.2 = 960$$ $$4800 \times 0.04 = 192$$ $$4800 \times 0.002 = 9.6$$ $$4800 \times 0.000296875 = 1.425$$ $$960 + 192 + 9.6 + 1.425 = 1163.025$$ $$4800 + 1163.025 = 5963.025$$

$A_B = \mathrm{R}5963.03$ (to 2 decimal places)

Comparison:
Capitec: $\mathrm{R}6528$
ABSA: $\mathrm{R}5963.03$
ABSA total is $\mathrm{R}564.97$ less.

Advice: Lihle should take the ABSA loan as the total repayment is lower.

\begin{array}{c} Capitec: R6528 \[0.5em] ABSA: R5963.03 \[0.5em] Choose ABSA \end{array}