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) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.

(2) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

(3) If Elizabeth borrowed $3450 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(4) Michelle had to pay $5247 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 7 years.

(7) How much loan did Robert borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5865 to clear it?

(8) How much loan did Andrew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8160 to clear it?

(9) Calculate the amount due if Susan borrowed a sum of $3650 at 4% simple interest for 3 years.

(10) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10600 to clear the loan, then find the time period of the loan.