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) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8750 to clear it?

(2) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 3% simple interest for 8 years.

(3) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 9% simple interest?

(4) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 4% simple interest.

(6) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 10% simple interest.

(7) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 4 years.

(8) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 8% simple interest?

(9) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.

(10) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.