Simple Interest
Math MCQs

Question :    If Michelle paid $5544 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $4950

Solution & Explanation

Solution

Given,

Amount (A) = $5544

Rate of Simple Interest (R) = 3%

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

$5544 = P (1 + 3% × 4)

⇒ $5544 = P (1 + ³/₁₀₀ × 4)

⇒ $5544 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $5544 = P (1 + ¹²/₁₀₀)

⇒ $5544 = P (^{100 + 12}/₁₀₀)

⇒ $5544 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $5544

⇒ P = ⁵⁵⁴⁴/_¹¹²/100

⇒ P = 5544 × ¹⁰⁰/₁₁₂

⇒ P = ^{5544 × 100}/₁₁₂

⇒ P = ⁵⁵⁴⁴⁰⁰/₁₁₂

⇒ 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 12

Thus, simple interest for 4 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₂

∴ If the Amount is 5544, then the Principal = ¹⁰⁰/₁₁₂ × 5544

= ^{100 × 5544}/₁₁₂

= ⁵⁵⁴⁴⁰⁰/₁₁₂

= 4950

Thus, Principal = $4950

Thus, the sum borrowed = $4950 Answer

Similar Questions

(1) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 4% simple interest?

(2) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 3 years.

(3) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.

(4) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 8 years.

(5) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.

(6) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 10% simple interest?

(7) If Michelle paid $5742 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(8) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.

(9) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9943 to clear the loan, then find the time period of the loan.

(10) How much loan did Mary borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6312.5 to clear it?