Simple Interest
Math MCQs

Question :    How much loan did Charles borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6490 to clear it?

Correct Answer  $5900

Solution & Explanation

Solution

Given,

Amount (A) = $6490

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

$6490 = P (1 + 2% × 5)

⇒ $6490 = P (1 + ²/₁₀₀ × 5)

⇒ $6490 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $6490 = P (1 + ¹⁰/₁₀₀)

⇒ $6490 = P (^{100 + 10}/₁₀₀)

⇒ $6490 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $6490

⇒ P = ⁶⁴⁹⁰/_¹¹⁰/100

⇒ P = 6490 × ¹⁰⁰/₁₁₀

⇒ P = ^{6490 × 100}/₁₁₀

⇒ P = ⁶⁴⁹⁰⁰⁰/₁₁₀

⇒ P = $5900

Thus, the sum borrowed (P) = $5900 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 6490, then the Principal = ¹⁰⁰/₁₁₀ × 6490

= ^{100 × 6490}/₁₁₀

= ⁶⁴⁹⁰⁰⁰/₁₁₀

= 5900

Thus, Principal = $5900

Thus, the sum borrowed = $5900 Answer

Similar Questions

(1) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 5% simple interest?

(2) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 7% simple interest.

(3) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 9% simple interest?

(4) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.

(5) William had to pay $3710 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

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

(7) In how much time a principal of $3100 will amount to $3472 at a simple interest of 3% per annum?

(8) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.

(9) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.

(10) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9231 to clear the loan, then find the time period of the loan.