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) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5960 to clear the loan, then find the time period of the loan.

(2) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 10% simple interest?

(3) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Charles borrowed a sum of $3900 at 3% simple interest for 3 years.

(5) What amount does James have to pay after 6 years if he takes a loan of $3000 at 9% simple interest?

(6) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 3 years.

(7) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 5% per annum?

(8) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 7 years.

(9) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 4% simple interest.

(10) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 6% simple interest?