Simple Interest
Math MCQs

Question :    If Susan paid $4088 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $3650

Solution & Explanation

Solution

Given,

Amount (A) = $4088

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

$4088 = P (1 + 3% × 4)

⇒ $4088 = P (1 + ³/₁₀₀ × 4)

⇒ $4088 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $4088 = P (1 + ¹²/₁₀₀)

⇒ $4088 = P (^{100 + 12}/₁₀₀)

⇒ $4088 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4088

⇒ P = ⁴⁰⁸⁸/_¹¹²/100

⇒ P = 4088 × ¹⁰⁰/₁₁₂

⇒ P = ^{4088 × 100}/₁₁₂

⇒ P = ⁴⁰⁸⁸⁰⁰/₁₁₂

⇒ P = $3650

Thus, the sum borrowed (P) = $3650 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 4088, then the Principal = ¹⁰⁰/₁₁₂ × 4088

= ^{100 × 4088}/₁₁₂

= ⁴⁰⁸⁸⁰⁰/₁₁₂

= 3650

Thus, Principal = $3650

Thus, the sum borrowed = $3650 Answer

Similar Questions

(1) In how much time a principal of $3100 will amount to $3472 at a simple interest of 3% per annum?

(2) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8415 to clear it?

(3) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7526 to clear the loan, then find the time period of the loan.

(4) If Joseph paid $3996 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(5) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.

(6) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.

(7) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $9200 to clear the loan, then find the time period of the loan.

(8) How much loan did Donna borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8562.5 to clear it?

(9) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 2% simple interest?

(10) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 3% simple interest?