Simple Interest
Math MCQs

Question :    Michelle had to pay $5544 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

Correct Answer  $4950

Solution & Explanation

Solution

Given,

Amount (A) = $5544

Rate of Simple Interest (R) = 4%

Time (T) = 3 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 + 4% × 3)

⇒ $5544 = P (1 + ⁴/₁₀₀ × 3)

⇒ $5544 = P (1 + ^{4 × 3}/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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

Calculation of the Amount

Since, in the question, time = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 4 = 12

Thus, simple interest for 3 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) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 3 years.

(2) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 10% simple interest?

(3) What amount does David have to pay after 6 years if he takes a loan of $3400 at 8% simple interest?

(4) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 2% simple interest?

(5) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $10450 to clear the loan, then find the time period of the loan.

(6) How much loan did Michelle borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7645 to clear it?

(7) Calculate the amount due if William borrowed a sum of $3500 at 7% simple interest for 4 years.

(8) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.

(9) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $8100 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 7 years.