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) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 4% simple interest?

(2) How much loan did Joshua borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8625 to clear it?

(3) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 2% simple interest?

(4) In how much time a principal of $3050 will amount to $3538 at a simple interest of 4% per annum?

(5) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 9% simple interest?

(6) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.

(7) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 8% simple interest?

(8) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 2% simple interest?

(9) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.

(10) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $5920 to clear the loan, then find the time period of the loan.