Simple Interest
Math MCQs

Question :    How much loan did Kenneth borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8050 to clear it?

Correct Answer  $7000

Solution & Explanation

Solution

Given,

Amount (A) = $8050

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

$8050 = P (1 + 3% × 5)

⇒ $8050 = P (1 + ³/₁₀₀ × 5)

⇒ $8050 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $8050 = P (1 + ¹⁵/₁₀₀)

⇒ $8050 = P (^{100 + 15}/₁₀₀)

⇒ $8050 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $8050

⇒ P = ⁸⁰⁵⁰/_¹¹⁵/100

⇒ P = 8050 × ¹⁰⁰/₁₁₅

⇒ P = ^{8050 × 100}/₁₁₅

⇒ P = ⁸⁰⁵⁰⁰⁰/₁₁₅

⇒ P = $7000

Thus, the sum borrowed (P) = $7000 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 8050, then the Principal = ¹⁰⁰/₁₁₅ × 8050

= ^{100 × 8050}/₁₁₅

= ⁸⁰⁵⁰⁰⁰/₁₁₅

= 7000

Thus, Principal = $7000

Thus, the sum borrowed = $7000 Answer

Similar Questions

(1) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 3% simple interest.

(2) 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?

(3) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 3% simple interest?

(4) How much loan did Kevin borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8165 to clear it?

(5) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 3% simple interest.

(6) Calculate the amount due if Thomas borrowed a sum of $3800 at 4% simple interest for 3 years.

(7) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 9% simple interest?

(8) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 7 years.

(9) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 9% simple interest?

(10) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.