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) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 9% simple interest.

(2) 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.

(3) If William paid $4060 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(4) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $9856 to clear the loan, then find the time period of the loan.

(5) If Ashley paid $4914 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(6) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 3 years.

(7) 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.

(8) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 6% simple interest?

(9) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 7% simple interest?

(10) If Joshua paid $5488 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.