Simple Interest
Math MCQs

Question :    How much loan did Susan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6215 to clear it?

Correct Answer  $5650

Solution & Explanation

Solution

Given,

Amount (A) = $6215

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

$6215 = P (1 + 2% × 5)

⇒ $6215 = P (1 + ²/₁₀₀ × 5)

⇒ $6215 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $6215 = P (1 + ¹⁰/₁₀₀)

⇒ $6215 = P (^{100 + 10}/₁₀₀)

⇒ $6215 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $6215

⇒ P = ⁶²¹⁵/_¹¹⁰/100

⇒ P = 6215 × ¹⁰⁰/₁₁₀

⇒ P = ^{6215 × 100}/₁₁₀

⇒ P = ⁶²¹⁵⁰⁰/₁₁₀

⇒ P = $5650

Thus, the sum borrowed (P) = $5650 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 6215, then the Principal = ¹⁰⁰/₁₁₀ × 6215

= ^{100 × 6215}/₁₁₀

= ⁶²¹⁵⁰⁰/₁₁₀

= 5650

Thus, Principal = $5650

Thus, the sum borrowed = $5650 Answer

Similar Questions

(1) What amount will be due after 2 years if James borrowed a sum of $3000 at a 9% simple interest?

(2) Calculate the amount due if Michael borrowed a sum of $3300 at 3% simple interest for 4 years.

(3) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.

(4) If Charles borrowed $3900 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(5) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 3% simple interest?

(6) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 3 years.

(8) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5440 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 2% simple interest.

(10) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 8% simple interest?