Simple Interest
Math MCQs

Question :    John had to pay $3488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

Correct Answer  $3200

Solution & Explanation

Solution

Given,

Amount (A) = $3488

Rate of Simple Interest (R) = 3%

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

$3488 = P (1 + 3% × 3)

⇒ $3488 = P (1 + ³/₁₀₀ × 3)

⇒ $3488 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $3488 = P (1 + ⁹/₁₀₀)

⇒ $3488 = P (^{100 + 9}/₁₀₀)

⇒ $3488 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $3488

⇒ P = ³⁴⁸⁸/_¹⁰⁹/100

⇒ P = 3488 × ¹⁰⁰/₁₀₉

⇒ P = ^{3488 × 100}/₁₀₉

⇒ P = ³⁴⁸⁸⁰⁰/₁₀₉

⇒ P = $3200

Thus, the sum borrowed (P) = $3200 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 9

Thus, simple interest for 3 years = 9

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 9 = 109

Calculation of the Principal

Now,

∵ If the Amount is 109, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₉

∴ If the Amount is 3488, then the Principal = ¹⁰⁰/₁₀₉ × 3488

= ^{100 × 3488}/₁₀₉

= ³⁴⁸⁸⁰⁰/₁₀₉

= 3200

Thus, Principal = $3200

Thus, the sum borrowed = $3200 Answer

Similar Questions

(1) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $9676 to clear the loan, then find the time period of the loan.

(2) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8493 to clear the loan, then find the time period of the loan.

(3) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 5% simple interest?

(4) Find the amount to be paid if James borrowed a sum of $5000 at 10% simple interest for 7 years.

(5) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 7 years.

(6) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 3 years.

(7) Matthew had to pay $4452 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(8) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 4 years.

(9) How much loan did Mary borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5555 to clear it?

(10) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 10% simple interest?