CAT 2025 Lesson : Interest & Growth - Past Questions

Observation/Strategy
1) Compound interest also grows at the same rate as that of the interest rate.
2) For the next $3$ years, the interest is higher by Rs. $5,000$ because interest rate is being applied on the first $3$ year's interest of Rs. $10,000$.

Let $r$ be the interest rate.

Interest for the first $3$ years $= \text{Rs.} 10,000$
Interest for the next $3$ years $= 25,000 - 10,000 = \text{Rs.} 15,000.$

From Point $2$, we form the following equation.

$10000 \times \left(1 + \dfrac{r}{100} \right)^{3} = 15000$

⇒ $\left(1 + \dfrac{r}{100} \right)^{3} = \dfrac{15000}{10000} = 1.5$

For a principal $p$, the interest at the end of $3$ years is Rs. $10,000$.

$A = p \left(1 +\dfrac{r}{100} \right)^{n}$

⇒ $p + 10000 = p \times \left(1 + \dfrac{r}{100} \right)^{3}$

⇒ $p + 10000 = p \times 1.5$

⇒ $0.5p = 10000$

⇒ $p = 20000$

Answer: ($3$) Rs. $20,000$

Observation/Strategy
$1$) We are asked to find the combined percentage applicable for the $3$ items - flat, car and shares. Therefore, these can be treated as one set of assets worth Rs. 70 lakhs. And, the bank deposit is Rs. $30$ lakhs.
$2$) The answers options are quite far apart (intervals of $15\%$). Therefore, we can approximate numbers.
$3$) All figures can be expressed as lakhs to simplify. So, let the amount won from lottery be Rs. $100$.

Initial investment $= 100$
Final Return $= 100 \times 1.05$ = 105

On simple interest at $12 \%$ p.a. for $3$ years amounts to $36 \%$ of interest. Compound interest will be a little more and approximated to 40%.

Amount earned from Bank deposit $= 30 \times (1.12)^{3} = 30 \times 1.4$ = 42

Revenue from other assets $= 105 - 42$ = 63

Revenue from other assets as $\%$ of original value $= \dfrac{63}{70} \times 100 \%$ = 90

Answer: ($3$) $90$ percent

Observation/Strategy
$1$) Interest is normally paid at maturity, as in the case of the ICICI loan.
$2$) In the Citibank loan, the interest is deducted/discounted at the time of issuance.

For instance, in a Rs. $100$ loan issued on discount basis at $19 \%$, the interest of Rs. $19$ is deducted from Rs. $100$ and disbursed.

Amount disbursed on discount basis $= 100 - 19 = \text{Rs}. 81$
Amount repaid on maturity $= \text{Rs}. 100$

So, interest of Rs. $19$ is effectively on a principal of Rs. $81$.

Effective interest rate $= \dfrac{19}{81} \times 100 \% = \dfrac{1900}{81} \%$ ~ 23.5

ICICI which currently has interest of $20 \%$ should increase its rate by 3.5%.

Answer: ($1$) Increase by $3.5 \%$