Simple Interest
Math MCQs

Question :    How much loan did Laura borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8635 to clear it?

Correct Answer  $7850

Solution & Explanation

Solution

Given,

Amount (A) = $8635

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

$8635 = P (1 + 2% × 5)

⇒ $8635 = P (1 + ²/₁₀₀ × 5)

⇒ $8635 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $8635 = P (1 + ¹⁰/₁₀₀)

⇒ $8635 = P (^{100 + 10}/₁₀₀)

⇒ $8635 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $8635

⇒ P = ⁸⁶³⁵/_¹¹⁰/100

⇒ P = 8635 × ¹⁰⁰/₁₁₀

⇒ P = ^{8635 × 100}/₁₁₀

⇒ P = ⁸⁶³⁵⁰⁰/₁₁₀

⇒ P = $7850

Thus, the sum borrowed (P) = $7850 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 8635, then the Principal = ¹⁰⁰/₁₁₀ × 8635

= ^{100 × 8635}/₁₁₀

= ⁸⁶³⁵⁰⁰/₁₁₀

= 7850

Thus, Principal = $7850

Thus, the sum borrowed = $7850 Answer

Similar Questions

(1) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10660 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.

(3) What amount will be due after 2 years if John borrowed a sum of $3100 at a 5% simple interest?

(4) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.

(5) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 3% simple interest.

(7) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 4% simple interest.

(8) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 8 years.

(9) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 2% simple interest.

(10) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.