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 Christopher have to pay after 6 years if he takes a loan of $4000 at 8% simple interest?

(2) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 8 years.

(3) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6267.5 to clear it?

(4) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 9% simple interest?

(5) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.

(6) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.

(7) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.

(9) If Betty paid $5100 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(10) Barbara had to pay $3869.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.