Simple Interest
Math MCQs

Question :    Christopher had to pay $4240 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

Correct Answer  $4000

Solution & Explanation

Solution

Given,

Amount (A) = $4240

Rate of Simple Interest (R) = 2%

Time (T) = 3 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

$4240 = P (1 + 2% × 3)

⇒ $4240 = P (1 + ²/₁₀₀ × 3)

⇒ $4240 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $4240 = P (1 + ⁶/₁₀₀)

⇒ $4240 = P (^{100 + 6}/₁₀₀)

⇒ $4240 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $4240

⇒ P = ⁴²⁴⁰/_¹⁰⁶/100

⇒ P = 4240 × ¹⁰⁰/₁₀₆

⇒ P = ^{4240 × 100}/₁₀₆

⇒ P = ⁴²⁴⁰⁰⁰/₁₀₆

⇒ 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 = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 2 = 6

Thus, simple interest for 3 years = 6

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 6 = 106

Calculation of the Principal

Now,

∵ If the Amount is 106, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₆

∴ If the Amount is 4240, then the Principal = ¹⁰⁰/₁₀₆ × 4240

= ^{100 × 4240}/₁₀₆

= ⁴²⁴⁰⁰⁰/₁₀₆

= 4000

Thus, Principal = $4000

Thus, the sum borrowed = $4000 Answer

Similar Questions

(1) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 4% simple interest?

(2) What amount does James have to pay after 5 years if he takes a loan of $3000 at 2% simple interest?

(3) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 7% simple interest?

(4) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7084 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Christopher borrowed a sum of $4000 at 10% simple interest for 4 years.

(6) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 4% simple interest?

(7) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.

(8) How much loan did Deborah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9312.5 to clear it?

(9) Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 4 years.

(10) Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 8 years.