Simple Interest
Math MCQs

Question :    If Christopher paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $4000

Solution & Explanation

Solution

Given,

Amount (A) = $4320

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

$4320 = P (1 + 2% × 4)

⇒ $4320 = P (1 + ²/₁₀₀ × 4)

⇒ $4320 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $4320 = P (1 + ⁸/₁₀₀)

⇒ $4320 = P (^{100 + 8}/₁₀₀)

⇒ $4320 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $4320

⇒ P = ⁴³²⁰/_¹⁰⁸/100

⇒ P = 4320 × ¹⁰⁰/₁₀₈

⇒ P = ^{4320 × 100}/₁₀₈

⇒ P = ⁴³²⁰⁰⁰/₁₀₈

⇒ 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 = 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 4320, then the Principal = ¹⁰⁰/₁₀₈ × 4320

= ^{100 × 4320}/₁₀₈

= ⁴³²⁰⁰⁰/₁₀₈

= 4000

Thus, Principal = $4000

Thus, the sum borrowed = $4000 Answer

Similar Questions

(1) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.

(2) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $10620 to clear the loan, then find the time period of the loan.

(3) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 7% simple interest for 4 years.

(5) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10595 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 5% simple interest.

(7) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 3 years.

(8) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9310 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 3% simple interest.

(10) In how much time a principal of $3100 will amount to $3286 at a simple interest of 2% per annum?