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) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 5% simple interest?

(2) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 7% simple interest.

(3) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 8 years.

(5) How much loan did Michael borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5830 to clear it?

(6) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8700 to clear it?

(7) How much loan did Barbara borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6937.5 to clear it?

(8) Linda had to pay $3752 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(9) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 6% simple interest.

(10) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 4 years.