Simple Interest
Math MCQs

Question :    If Christopher paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $4000

Solution & Explanation

Solution

Given,

Amount (A) = $4320

Rate of Simple Interest (R) = 2%

Time (T) = 4 years

Thus, Principal (P) = ?

Method (1) Using Formula

Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given

Formula to find the Principal (P)

Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)

⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]

⇒ A = P (1 + RT)

Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given

In the given question, we need to find the Principal (P)

Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get

$4320 = P (1 + 2% × 4)

⇒ $4320 = P (1 + ²/₁₀₀ × 4)

⇒ $4320 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $4320 = P (1 + ⁸/₁₀₀)

⇒ $4320 = P (^{100 + 8}/₁₀₀)

⇒ $4320 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $4320

⇒ P = ⁴³²⁰/_¹⁰⁸/100

⇒ P = 4320 × ¹⁰⁰/₁₀₈

⇒ P = ^{4320 × 100}/₁₀₈

⇒ P = ⁴³²⁰⁰⁰/₁₀₈

⇒ P = $4000

Thus, the sum borrowed (P) = $4000 Answer

Method (1) Using Unitary Method

Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given

Calculation of the Simple Interest

Let, the principal = 100

Here, since rate of simple interest = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

Calculation of the Amount

Since, in the question, time = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 2 = 8

Thus, simple interest for 4 years = 8

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 8 = 108

Calculation of the Principal

Now,

∵ If the Amount is 108, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₈

∴ If the Amount is 4320, then the Principal = ¹⁰⁰/₁₀₈ × 4320

= ^{100 × 4320}/₁₀₈

= ⁴³²⁰⁰⁰/₁₀₈

= 4000

Thus, Principal = $4000

Thus, the sum borrowed = $4000 Answer

Similar Questions

(1) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8688 to clear the loan, then find the time period of the loan.

(2) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 10% simple interest?

(3) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 5% simple interest?

(4) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 8 years.

(5) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 4 years.

(6) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 6% simple interest?

(7) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $5964 to clear the loan, then find the time period of the loan.

(8) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 8% simple interest?

(9) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9184 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if John borrowed a sum of $5200 at 8% simple interest for 8 years.