Simple Interest
Math MCQs

Question :    How much loan did Jason borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8855 to clear it?

Correct Answer  $7700

Solution & Explanation

Solution

Given,

Amount (A) = $8855

Rate of Simple Interest (R) = 3%

Time (T) = 5 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

$8855 = P (1 + 3% × 5)

⇒ $8855 = P (1 + ³/₁₀₀ × 5)

⇒ $8855 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $8855 = P (1 + ¹⁵/₁₀₀)

⇒ $8855 = P (^{100 + 15}/₁₀₀)

⇒ $8855 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $8855

⇒ P = ⁸⁸⁵⁵/_¹¹⁵/100

⇒ P = 8855 × ¹⁰⁰/₁₁₅

⇒ P = ^{8855 × 100}/₁₁₅

⇒ P = ⁸⁸⁵⁵⁰⁰/₁₁₅

⇒ P = $7700

Thus, the sum borrowed (P) = $7700 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 = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 8855, then the Principal = ¹⁰⁰/₁₁₅ × 8855

= ^{100 × 8855}/₁₁₅

= ⁸⁸⁵⁵⁰⁰/₁₁₅

= 7700

Thus, Principal = $7700

Thus, the sum borrowed = $7700 Answer

Similar Questions

(1) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 3 years.

(2) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 2% simple interest?

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

(4) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.

(5) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 8% simple interest?

(6) If Michelle paid $5940 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(7) Calculate the amount due if Robert borrowed a sum of $3100 at 8% simple interest for 3 years.

(8) Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 4 years.

(9) How much loan did Jason borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9625 to clear it?

(10) If Donna paid $5626 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.