Simple Interest
Math MCQs

Question :    How much loan did Sharon borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8912.5 to clear it?

Correct Answer  $7750

Solution & Explanation

Solution

Given,

Amount (A) = $8912.5

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

$8912.5 = P (1 + 3% × 5)

⇒ $8912.5 = P (1 + ³/₁₀₀ × 5)

⇒ $8912.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $8912.5 = P (1 + ¹⁵/₁₀₀)

⇒ $8912.5 = P (^{100 + 15}/₁₀₀)

⇒ $8912.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $8912.5

⇒ P = ^8912.5/_¹¹⁵/100

⇒ P = 8912.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{8912.5 × 100}/₁₁₅

⇒ P = ⁸⁹¹²⁵⁰/₁₁₅

⇒ P = $7750

Thus, the sum borrowed (P) = $7750 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 8912.5, then the Principal = ¹⁰⁰/₁₁₅ × 8912.5

= ^{100 × 8912.5}/₁₁₅

= ⁸⁹¹²⁵⁰/₁₁₅

= 7750

Thus, Principal = $7750

Thus, the sum borrowed = $7750 Answer

Similar Questions

(1) How much loan did Laura borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8635 to clear it?

(2) Steven had to pay $4876 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 6% simple interest for 7 years.

(4) What amount does David have to pay after 6 years if he takes a loan of $3400 at 2% simple interest?

(5) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 7% simple interest?

(6) How much loan did Jason borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9240 to clear it?

(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 8 years.

(8) Calculate the amount due if Thomas borrowed a sum of $3800 at 7% simple interest for 3 years.

(9) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 5% simple interest?

(10) If Patricia paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.