Simple Interest
Math MCQs

Question :    How much loan did Kevin borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8520 to clear it?

Correct Answer  $7100

Solution & Explanation

Solution

Given,

Amount (A) = $8520

Rate of Simple Interest (R) = 4%

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

$8520 = P (1 + 4% × 5)

⇒ $8520 = P (1 + ⁴/₁₀₀ × 5)

⇒ $8520 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $8520 = P (1 + ²⁰/₁₀₀)

⇒ $8520 = P (^{100 + 20}/₁₀₀)

⇒ $8520 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $8520

⇒ P = ⁸⁵²⁰/_¹²⁰/100

⇒ P = 8520 × ¹⁰⁰/₁₂₀

⇒ P = ^{8520 × 100}/₁₂₀

⇒ P = ⁸⁵²⁰⁰⁰/₁₂₀

⇒ 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 20

Thus, simple interest for 5 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 8520, then the Principal = ¹⁰⁰/₁₂₀ × 8520

= ^{100 × 8520}/₁₂₀

= ⁸⁵²⁰⁰⁰/₁₂₀

= 7100

Thus, Principal = $7100

Thus, the sum borrowed = $7100 Answer

Similar Questions

(1) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 8 years.

(2) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 10% simple interest.

(3) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 10% simple interest.

(4) Calculate the amount due if Richard borrowed a sum of $3600 at 4% simple interest for 3 years.

(5) Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 3 years.

(6) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 8 years.

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

(8) If William paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(9) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.

(10) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.