Simple Interest
Math MCQs

Question :    If Karen paid $4266 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $3950

Solution & Explanation

Solution

Given,

Amount (A) = $4266

Rate of Simple Interest (R) = 2%

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

$4266 = P (1 + 2% × 4)

⇒ $4266 = P (1 + ²/₁₀₀ × 4)

⇒ $4266 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $4266 = P (1 + ⁸/₁₀₀)

⇒ $4266 = P (^{100 + 8}/₁₀₀)

⇒ $4266 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $4266

⇒ P = ⁴²⁶⁶/_¹⁰⁸/100

⇒ P = 4266 × ¹⁰⁰/₁₀₈

⇒ P = ^{4266 × 100}/₁₀₈

⇒ P = ⁴²⁶⁶⁰⁰/₁₀₈

⇒ P = $3950

Thus, the sum borrowed (P) = $3950 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 8

Thus, simple interest for 4 years = 8

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 8 = 108

Calculation of the Principal

Now,

∵ If the Amount is 108, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₈

∴ If the Amount is 4266, then the Principal = ¹⁰⁰/₁₀₈ × 4266

= ^{100 × 4266}/₁₀₈

= ⁴²⁶⁶⁰⁰/₁₀₈

= 3950

Thus, Principal = $3950

Thus, the sum borrowed = $3950 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 8% simple interest.

(2) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9774 to clear the loan, then find the time period of the loan.

(3) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Sarah borrowed a sum of $3850 at 9% simple interest for 3 years.

(5) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.

(6) Betty had to pay $4632.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(7) If Kimberly paid $5580 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(8) If David paid $3808 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(9) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 2% simple interest?

(10) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.