Simple Interest
Math MCQs

Question :    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?

Correct Answer  $6900

Solution & Explanation

Solution

Given,

Amount (A) = $7935

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

$7935 = P (1 + 3% × 5)

⇒ $7935 = P (1 + ³/₁₀₀ × 5)

⇒ $7935 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $7935 = P (1 + ¹⁵/₁₀₀)

⇒ $7935 = P (^{100 + 15}/₁₀₀)

⇒ $7935 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $7935

⇒ P = ⁷⁹³⁵/_¹¹⁵/100

⇒ P = 7935 × ¹⁰⁰/₁₁₅

⇒ P = ^{7935 × 100}/₁₁₅

⇒ P = ⁷⁹³⁵⁰⁰/₁₁₅

⇒ P = $6900

Thus, the sum borrowed (P) = $6900 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 7935, then the Principal = ¹⁰⁰/₁₁₅ × 7935

= ^{100 × 7935}/₁₁₅

= ⁷⁹³⁵⁰⁰/₁₁₅

= 6900

Thus, Principal = $6900

Thus, the sum borrowed = $6900 Answer

Similar Questions

(1) 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.

(2) Linda had to pay $3551 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(3) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 2% simple interest?

(4) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 3 years.

(5) If Michelle paid $5544 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(6) Find the amount to be paid if Susan borrowed a sum of $5650 at 7% simple interest for 8 years.

(7) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 8% simple interest?

(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 4% simple interest for 8 years.

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

(10) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.