Simple Interest
Math MCQs

Question :    If James paid $3240 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $3000

Solution & Explanation

Solution

Given,

Amount (A) = $3240

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

$3240 = P (1 + 2% × 4)

⇒ $3240 = P (1 + ²/₁₀₀ × 4)

⇒ $3240 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $3240 = P (1 + ⁸/₁₀₀)

⇒ $3240 = P (^{100 + 8}/₁₀₀)

⇒ $3240 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $3240

⇒ P = ³²⁴⁰/_¹⁰⁸/100

⇒ P = 3240 × ¹⁰⁰/₁₀₈

⇒ P = ^{3240 × 100}/₁₀₈

⇒ P = ³²⁴⁰⁰⁰/₁₀₈

⇒ P = $3000

Thus, the sum borrowed (P) = $3000 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 3240, then the Principal = ¹⁰⁰/₁₀₈ × 3240

= ^{100 × 3240}/₁₀₈

= ³²⁴⁰⁰⁰/₁₀₈

= 3000

Thus, Principal = $3000

Thus, the sum borrowed = $3000 Answer

Similar Questions

(1) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 8 years.

(2) Betty had to pay $4760 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(3) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.

(4) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 4% simple interest.

(5) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 10% simple interest?

(6) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.

(7) What amount does James have to pay after 6 years if he takes a loan of $3000 at 7% simple interest?

(8) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 6% simple interest?

(9) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 3 years.

(10) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 3 years.