Simple Interest
Math MCQs

Question :    How much loan did David borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5940 to clear it?

Correct Answer  $5400

Solution & Explanation

Solution

Given,

Amount (A) = $5940

Rate of Simple Interest (R) = 2%

Time (T) = 5 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

$5940 = P (1 + 2% × 5)

⇒ $5940 = P (1 + ²/₁₀₀ × 5)

⇒ $5940 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $5940 = P (1 + ¹⁰/₁₀₀)

⇒ $5940 = P (^{100 + 10}/₁₀₀)

⇒ $5940 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $5940

⇒ P = ⁵⁹⁴⁰/_¹¹⁰/100

⇒ P = 5940 × ¹⁰⁰/₁₁₀

⇒ P = ^{5940 × 100}/₁₁₀

⇒ P = ⁵⁹⁴⁰⁰⁰/₁₁₀

⇒ P = $5400

Thus, the sum borrowed (P) = $5400 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 = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 2 = 10

Thus, simple interest for 5 years = 10

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 10 = 110

Calculation of the Principal

Now,

∵ If the Amount is 110, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₀

∴ If the Amount is 5940, then the Principal = ¹⁰⁰/₁₁₀ × 5940

= ^{100 × 5940}/₁₁₀

= ⁵⁹⁴⁰⁰⁰/₁₁₀

= 5400

Thus, Principal = $5400

Thus, the sum borrowed = $5400 Answer

Similar Questions

(1) If Paul paid $5452 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(2) Daniel had to pay $4715 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(3) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7301 to clear the loan, then find the time period of the loan.

(4) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 10% simple interest?

(5) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $11152 to clear the loan, then find the time period of the loan.

(6) Richard had to pay $3816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(7) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $7888 to clear the loan, then find the time period of the loan.

(8) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 3% simple interest?

(9) In how much time a principal of $3200 will amount to $3520 at a simple interest of 5% per annum?

(10) Calculate the amount due if Patricia borrowed a sum of $3150 at 7% simple interest for 3 years.