Simple Interest
Math MCQs

Question :    If Christopher paid $4480 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $4000

Solution & Explanation

Solution

Given,

Amount (A) = $4480

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

$4480 = P (1 + 3% × 4)

⇒ $4480 = P (1 + ³/₁₀₀ × 4)

⇒ $4480 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $4480 = P (1 + ¹²/₁₀₀)

⇒ $4480 = P (^{100 + 12}/₁₀₀)

⇒ $4480 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4480

⇒ P = ⁴⁴⁸⁰/_¹¹²/100

⇒ P = 4480 × ¹⁰⁰/₁₁₂

⇒ P = ^{4480 × 100}/₁₁₂

⇒ P = ⁴⁴⁸⁰⁰⁰/₁₁₂

⇒ P = $4000

Thus, the sum borrowed (P) = $4000 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 4480, then the Principal = ¹⁰⁰/₁₁₂ × 4480

= ^{100 × 4480}/₁₁₂

= ⁴⁴⁸⁰⁰⁰/₁₁₂

= 4000

Thus, Principal = $4000

Thus, the sum borrowed = $4000 Answer

Similar Questions

(1) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7301 to clear the loan, then find the time period of the loan.

(2) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 6% simple interest?

(3) Calculate the amount due if Jessica borrowed a sum of $3750 at 7% simple interest for 4 years.

(4) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.

(5) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.

(6) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8970 to clear it?

(7) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.

(9) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.

(10) How much loan did Steven borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7260 to clear it?