Simple Interest
Math MCQs

Question :    If Michelle paid $5940 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $4950

Solution & Explanation

Solution

Given,

Amount (A) = $5940

Rate of Simple Interest (R) = 5%

Time (T) = 4 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

$5940 = P (1 + 5% × 4)

⇒ $5940 = P (1 + ⁵/₁₀₀ × 4)

⇒ $5940 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $5940 = P (1 + ²⁰/₁₀₀)

⇒ $5940 = P (^{100 + 20}/₁₀₀)

⇒ $5940 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $5940

⇒ P = ⁵⁹⁴⁰/_¹²⁰/100

⇒ P = 5940 × ¹⁰⁰/₁₂₀

⇒ P = ^{5940 × 100}/₁₂₀

⇒ P = ⁵⁹⁴⁰⁰⁰/₁₂₀

⇒ P = $4950

Thus, the sum borrowed (P) = $4950 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 = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 5 = 20

Thus, simple interest for 4 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 5940, then the Principal = ¹⁰⁰/₁₂₀ × 5940

= ^{100 × 5940}/₁₂₀

= ⁵⁹⁴⁰⁰⁰/₁₂₀

= 4950

Thus, Principal = $4950

Thus, the sum borrowed = $4950 Answer

Similar Questions

(1) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 7 years.

(2) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.

(4) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.

(5) How much loan did Joshua borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7935 to clear it?

(6) Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 7 years.

(7) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.

(8) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7084 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 8 years.

(10) Emily had to pay $5035 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.