Simple Interest
Math MCQs

Question :    How much loan did Kevin borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8875 to clear it?

Correct Answer  $7100

Solution & Explanation

Solution

Given,

Amount (A) = $8875

Rate of Simple Interest (R) = 5%

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

$8875 = P (1 + 5% × 5)

⇒ $8875 = P (1 + ⁵/₁₀₀ × 5)

⇒ $8875 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $8875 = P (1 + ²⁵/₁₀₀)

⇒ $8875 = P (^{100 + 25}/₁₀₀)

⇒ $8875 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $8875

⇒ P = ⁸⁸⁷⁵/_¹²⁵/100

⇒ P = 8875 × ¹⁰⁰/₁₂₅

⇒ P = ^{8875 × 100}/₁₂₅

⇒ P = ⁸⁸⁷⁵⁰⁰/₁₂₅

⇒ P = $7100

Thus, the sum borrowed (P) = $7100 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 8875, then the Principal = ¹⁰⁰/₁₂₅ × 8875

= ^{100 × 8875}/₁₂₅

= ⁸⁸⁷⁵⁰⁰/₁₂₅

= 7100

Thus, Principal = $7100

Thus, the sum borrowed = $7100 Answer

Similar Questions

(1) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 7 years.

(2) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 4 years.

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

(4) What amount does William have to pay after 6 years if he takes a loan of $3500 at 8% simple interest?

(5) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10106 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 4% simple interest.

(7) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.

(8) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.

(9) What amount does David have to pay after 6 years if he takes a loan of $3400 at 5% simple interest?

(10) Susan had to pay $4197.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.