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) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8140 to clear the loan, then find the time period of the loan.

(2) How much loan did Jacob borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8800 to clear it?

(3) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 4% simple interest.

(4) Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 3 years.

(5) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 4 years.

(6) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.

(7) How much loan did Ashley borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7860 to clear it?

(8) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.

(10) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.