Simple Interest
Math MCQs

Question :    How much loan did Timothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8510 to clear it?

Correct Answer  $7400

Solution & Explanation

Solution

Given,

Amount (A) = $8510

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

$8510 = P (1 + 3% × 5)

⇒ $8510 = P (1 + ³/₁₀₀ × 5)

⇒ $8510 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $8510 = P (1 + ¹⁵/₁₀₀)

⇒ $8510 = P (^{100 + 15}/₁₀₀)

⇒ $8510 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $8510

⇒ P = ⁸⁵¹⁰/_¹¹⁵/100

⇒ P = 8510 × ¹⁰⁰/₁₁₅

⇒ P = ^{8510 × 100}/₁₁₅

⇒ P = ⁸⁵¹⁰⁰⁰/₁₁₅

⇒ P = $7400

Thus, the sum borrowed (P) = $7400 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 8510, then the Principal = ¹⁰⁰/₁₁₅ × 8510

= ^{100 × 8510}/₁₁₅

= ⁸⁵¹⁰⁰⁰/₁₁₅

= 7400

Thus, Principal = $7400

Thus, the sum borrowed = $7400 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.

(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 8 years.

(3) David had to pay $3808 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(4) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 8 years.

(5) What amount does John have to pay after 6 years if he takes a loan of $3200 at 4% simple interest?

(6) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.

(8) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.

(9) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 8% simple interest?

(10) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 4% simple interest.