Simple Interest
Math MCQs

Question :    Joshua had to pay $5341 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  $4900

Solution & Explanation

Solution

Given,

Amount (A) = $5341

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

$5341 = P (1 + 3% × 3)

⇒ $5341 = P (1 + ³/₁₀₀ × 3)

⇒ $5341 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $5341 = P (1 + ⁹/₁₀₀)

⇒ $5341 = P (^{100 + 9}/₁₀₀)

⇒ $5341 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $5341

⇒ P = ⁵³⁴¹/_¹⁰⁹/100

⇒ P = 5341 × ¹⁰⁰/₁₀₉

⇒ P = ^{5341 × 100}/₁₀₉

⇒ P = ⁵³⁴¹⁰⁰/₁₀₉

⇒ P = $4900

Thus, the sum borrowed (P) = $4900 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 5341, then the Principal = ¹⁰⁰/₁₀₉ × 5341

= ^{100 × 5341}/₁₀₉

= ⁵³⁴¹⁰⁰/₁₀₉

= 4900

Thus, Principal = $4900

Thus, the sum borrowed = $4900 Answer

Similar Questions

(1) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 2% simple interest?

(2) Calculate the amount due if Robert borrowed a sum of $3100 at 2% simple interest for 3 years.

(3) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.

(4) How much loan did Joshua borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7935 to clear it?

(5) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 5% simple interest?

(6) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 4% simple interest?

(7) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 6% simple interest?

(8) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5920 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 2% simple interest for 4 years.

(10) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 7% simple interest?