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) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 10% simple interest.

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

(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 7 years.

(4) In how much time a principal of $3050 will amount to $3324.5 at a simple interest of 3% per annum?

(5) Kimberly had to pay $5208 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(6) Calculate the amount due if Karen borrowed a sum of $3950 at 7% simple interest for 4 years.

(7) If Andrew paid $5184 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(8) What amount does John have to pay after 6 years if he takes a loan of $3200 at 8% simple interest?

(9) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 3% simple interest.

(10) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.