Simple Interest
Math MCQs

Question :    If Margaret paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $4350

Solution & Explanation

Solution

Given,

Amount (A) = $4698

Rate of Simple Interest (R) = 2%

Time (T) = 4 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

$4698 = P (1 + 2% × 4)

⇒ $4698 = P (1 + ²/₁₀₀ × 4)

⇒ $4698 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $4698 = P (1 + ⁸/₁₀₀)

⇒ $4698 = P (^{100 + 8}/₁₀₀)

⇒ $4698 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $4698

⇒ P = ⁴⁶⁹⁸/_¹⁰⁸/100

⇒ P = 4698 × ¹⁰⁰/₁₀₈

⇒ P = ^{4698 × 100}/₁₀₈

⇒ P = ⁴⁶⁹⁸⁰⁰/₁₀₈

⇒ P = $4350

Thus, the sum borrowed (P) = $4350 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 = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 2 = 8

Thus, simple interest for 4 years = 8

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 8 = 108

Calculation of the Principal

Now,

∵ If the Amount is 108, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₈

∴ If the Amount is 4698, then the Principal = ¹⁰⁰/₁₀₈ × 4698

= ^{100 × 4698}/₁₀₈

= ⁴⁶⁹⁸⁰⁰/₁₀₈

= 4350

Thus, Principal = $4350

Thus, the sum borrowed = $4350 Answer

Similar Questions

(1) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.

(2) How much loan did George borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8030 to clear it?

(3) In how much time a principal of $3000 will amount to $3300 at a simple interest of 5% per annum?

(4) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6552 to clear the loan, then find the time period of the loan.

(5) How much loan did James borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5750 to clear it?

(6) Calculate the amount due if James borrowed a sum of $3000 at 2% simple interest for 3 years.

(7) Find the amount to be paid if Susan borrowed a sum of $5650 at 2% simple interest for 8 years.

(8) What amount will be due after 2 years if John borrowed a sum of $3100 at a 7% simple interest?

(9) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 3 years.

(10) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.