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: $P = R4800$

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

Step 1: Simple interest formula
$I = P \times r \times t$
Substitute $P = 4800$, $r = 0.12$, $t = 3$:
$I = 4800 \times 0.12 \times 3$
$4800 \times 0.12 = 576$
$576 \times 3 = 1728$
$I = R1728$

Step 2: Total repayment
$A_A = P + I$
$A_A = 4800 + 1728 = 6528$
$A_A = R6528$
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
$A_B = 4800 \times 1.242296875$
$4800 \times 1 = 4800$
$4800 \times 0.242296875$
$4800 \times 0.2 = 960$
$4800 \times 0.04 = 192$
$4800 \times 0.002 = 9.6$
$4800 \times 0.000296875 = 1.425$
$960 + 192 + 9.6 + 1.425 = 1163.025$
$4800 + 1163.025 = 5963.025$
$A_B = R5963.03$ (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}}