CAT 2025 Lesson : Interest & Growth - Advanced Simple Interest

What investment would result in Rs. $13,440$ in $2$ years at $6 \%$ per annum of simple interest?

Solution

$13440 = p + \dfrac{p \times 2 \times 6}{100} = p + \dfrac{3p}{25} = \dfrac{28p}{25}$

⇒ $p = 13440 \times \dfrac{25}{28} = 480 \times 25 =$ Rs. $12,000$

Alternatively, you can convert the interest from percentage to decimal form.

$13440 = p + (p \times 2 \times 0.06) = 1.12 p$

⇒ $p = \dfrac{13440}{1.12} =$ Rs. $12,000$

Answer: Rs. $12,000$

Jasprit invested Rs. $1,600$ for a period of $3$ years and Rs. $2,000$ for a period of $5$ years. Both the deposits yielded simple interest at the same rate. If the total interest received from the two deposits was Rs. $1,110$, what was the rate of interest?

Solution

Let the rate of interest be $r \%$.

$1110 = \dfrac{1600 \times 3 \times r}{100} + \dfrac{2000 \times 5 \times r}{100}$

⇒ $1110 = 48r + 100r$

⇒ $r = \dfrac{1110}{148} = \dfrac{30}{4} = 7.5$

Answer: $7.5 \%$

Moshe lent to George and Michael sums of money in the ratio of $4 : 5$. If the tenure of these loans were in the ratio of $4 : 3$ and the simple interest earned was in the ratio of $8 : 3$, then what was the ratio of the interest rates?

Solution

As principals, tenures and interest amounts are in ratios, we can use common variables.

Let the principals lent to George and Michael be $4p$ and $5p$ respectively.
Let the tenure of the loans be $4n$ and $3n$ respectively.
Let the simple interest earned be $8s$ and $3s$ respectively.

Let the rate of interest on sums lent to George and Michael be $x$ and $y$ respectively.

$\dfrac{\dfrac{4p \times 4n \times x}{100}}{\dfrac{5p \times 3n \times y}{100}} = \dfrac{8s}{3s}$

$\dfrac{x}{y} = \dfrac{8}{3} \times \dfrac{15}{16} = \dfrac{5}{2}$

Answer: $5 : 2$

Jacinda invested a total of Rs. $14,00,000$ in three deposits yielding a simple interest of $6 \%$ per annum, such that the interest earned from the first deposit in $8$ years equalled the interest earned from the second deposit in $10$ years, which in turn equalled the interest earned from the third deposit in $15$ years. What was the principal amount invested in the second deposit?

Solution

Let $a$, $b$ and $c$ be the amounts invested in the three deposits respectively.

$a + b + c = 1400000 \longrightarrow (1)$

Let $K$ be the simple interest earned from each of them from their respective time periods.

$\dfrac{a \times 8 \times 6}{100} = \dfrac{b \times 10 \times 6}{100} = \dfrac{c \times 15 \times 6}{100} = K$

⇒ $a = \dfrac{100K}{48}, b = \dfrac{100K}{60}, c = \dfrac{100K}{90}$

Substituting in ($1$),

$\dfrac{100K}{48} + \dfrac{100K}{60} + \dfrac{100K}{90} = 1400000$

⇒ $\dfrac{K}{6} \times \left(\dfrac{1}{8} + \dfrac{1}{10} + \dfrac{1}{5} \right) = 14000$

⇒ $K \times \left(\dfrac{15 + 12 + 8}{120} \right) = 84000$

$K = 84000 \times \dfrac{120}{35} = 288000$

$b = \dfrac{100 \times 288000}{60} = 480000$

Answer: Rs. $4,80,000$