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 does Barbara have to pay after 6 years if he takes a loan of $3550 at 3% simple interest?

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

(3) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 6% simple interest.

(4) How much loan did Sarah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6727.5 to clear it?

(5) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 4% simple interest?

(6) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9937.5 to clear it?

(7) How much loan did Richard borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6440 to clear it?

(8) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.

(9) How much loan did Melissa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8452.5 to clear it?

(10) What amount will be due after 2 years if William borrowed a sum of $3250 at a 8% simple interest?