Simple Interest
Math MCQs

Question :    Christopher had to pay $4480 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  $4000

Solution & Explanation

Solution

Given,

Amount (A) = $4480

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

$4480 = P (1 + 4% × 3)

⇒ $4480 = P (1 + ⁴/₁₀₀ × 3)

⇒ $4480 = P (1 + ^{4 × 3}/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 = 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 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) If Jennifer paid $3770 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(2) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $10758 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 7 years.

(4) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 4% simple interest.

(6) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 7% simple interest?

(7) If William paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(8) If Richard borrowed $3600 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(9) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $12540 to clear the loan, then find the time period of the loan.

(10) Daniel had to pay $4715 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.