Simple Interest
Math MCQs

Question :    If Robert paid $3472 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $3100

Solution & Explanation

Solution

Given,

Amount (A) = $3472

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

$3472 = P (1 + 3% × 4)

⇒ $3472 = P (1 + ³/₁₀₀ × 4)

⇒ $3472 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $3472 = P (1 + ¹²/₁₀₀)

⇒ $3472 = P (^{100 + 12}/₁₀₀)

⇒ $3472 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $3472

⇒ P = ³⁴⁷²/_¹¹²/100

⇒ P = 3472 × ¹⁰⁰/₁₁₂

⇒ P = ^{3472 × 100}/₁₁₂

⇒ P = ³⁴⁷²⁰⁰/₁₁₂

⇒ P = $3100

Thus, the sum borrowed (P) = $3100 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 3472, then the Principal = ¹⁰⁰/₁₁₂ × 3472

= ^{100 × 3472}/₁₁₂

= ³⁴⁷²⁰⁰/₁₁₂

= 3100

Thus, Principal = $3100

Thus, the sum borrowed = $3100 Answer

Similar Questions

(1) Calculate the amount due if Michael borrowed a sum of $3300 at 8% simple interest for 4 years.

(2) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 8 years.

(3) What amount does James have to pay after 6 years if he takes a loan of $3000 at 9% simple interest?

(4) Sarah had to pay $4196.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

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

(6) If Paul paid $5264 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(7) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 3 years.

(8) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.

(9) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 7 years.