Simple Interest
Math MCQs

Question :    How much loan did Karen borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6545 to clear it?

Correct Answer  $5950

Solution & Explanation

Solution

Given,

Amount (A) = $6545

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

$6545 = P (1 + 2% × 5)

⇒ $6545 = P (1 + ²/₁₀₀ × 5)

⇒ $6545 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $6545 = P (1 + ¹⁰/₁₀₀)

⇒ $6545 = P (^{100 + 10}/₁₀₀)

⇒ $6545 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $6545

⇒ P = ⁶⁵⁴⁵/_¹¹⁰/100

⇒ P = 6545 × ¹⁰⁰/₁₁₀

⇒ P = ^{6545 × 100}/₁₁₀

⇒ P = ⁶⁵⁴⁵⁰⁰/₁₁₀

⇒ P = $5950

Thus, the sum borrowed (P) = $5950 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 6545, then the Principal = ¹⁰⁰/₁₁₀ × 6545

= ^{100 × 6545}/₁₁₀

= ⁶⁵⁴⁵⁰⁰/₁₁₀

= 5950

Thus, Principal = $5950

Thus, the sum borrowed = $5950 Answer

Similar Questions

(1) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.

(2) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 8% simple interest?

(3) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9028 to clear the loan, then find the time period of the loan.

(4) If Joseph paid $4440 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(5) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.

(6) How much loan did Laura borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9027.5 to clear it?

(7) Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 8 years.

(8) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 10% simple interest?

(9) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $6854 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.