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) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.

(3) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.

(4) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 4% simple interest?

(5) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 3% simple interest?

(6) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.

(7) What amount does David have to pay after 6 years if he takes a loan of $3400 at 2% simple interest?

(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 6% simple interest for 7 years.

(9) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $13400 to clear the loan, then find the time period of the loan.

(10) If Ashley paid $4914 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.