Simple Interest
Math MCQs

Question :    If Donald paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $4500

Solution & Explanation

Solution

Given,

Amount (A) = $4860

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

$4860 = P (1 + 2% × 4)

⇒ $4860 = P (1 + ²/₁₀₀ × 4)

⇒ $4860 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $4860 = P (1 + ⁸/₁₀₀)

⇒ $4860 = P (^{100 + 8}/₁₀₀)

⇒ $4860 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $4860

⇒ P = ⁴⁸⁶⁰/_¹⁰⁸/100

⇒ P = 4860 × ¹⁰⁰/₁₀₈

⇒ P = ^{4860 × 100}/₁₀₈

⇒ P = ⁴⁸⁶⁰⁰⁰/₁₀₈

⇒ P = $4500

Thus, the sum borrowed (P) = $4500 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 4860, then the Principal = ¹⁰⁰/₁₀₈ × 4860

= ^{100 × 4860}/₁₀₈

= ⁴⁸⁶⁰⁰⁰/₁₀₈

= 4500

Thus, Principal = $4500

Thus, the sum borrowed = $4500 Answer

Similar Questions

(1) What amount will be due after 2 years if William borrowed a sum of $3250 at a 8% simple interest?

(2) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Jessica borrowed a sum of $3750 at 9% simple interest for 3 years.

(4) Emily had to pay $5320 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(5) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.

(6) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.

(7) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 4% simple interest?

(8) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 4% simple interest.

(9) If David borrowed $3400 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(10) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.