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) How much loan did Mary borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6060 to clear it?

(2) If Michael paid $3564 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(3) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.

(4) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.

(5) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.

(6) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8288 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.

(8) Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 8 years.

(9) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 3 years.

(10) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 7 years.