Simple Interest
Math MCQs

Question :    If Mary paid $3294 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $3050

Solution & Explanation

Solution

Given,

Amount (A) = $3294

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

$3294 = P (1 + 2% × 4)

⇒ $3294 = P (1 + ²/₁₀₀ × 4)

⇒ $3294 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $3294 = P (1 + ⁸/₁₀₀)

⇒ $3294 = P (^{100 + 8}/₁₀₀)

⇒ $3294 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $3294

⇒ P = ³²⁹⁴/_¹⁰⁸/100

⇒ P = 3294 × ¹⁰⁰/₁₀₈

⇒ P = ^{3294 × 100}/₁₀₈

⇒ P = ³²⁹⁴⁰⁰/₁₀₈

⇒ P = $3050

Thus, the sum borrowed (P) = $3050 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 3294, then the Principal = ¹⁰⁰/₁₀₈ × 3294

= ^{100 × 3294}/₁₀₈

= ³²⁹⁴⁰⁰/₁₀₈

= 3050

Thus, Principal = $3050

Thus, the sum borrowed = $3050 Answer

Similar Questions

(1) Find the amount to be paid if Richard borrowed a sum of $5600 at 10% simple interest for 7 years.

(2) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 4% simple interest.

(3) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.

(4) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.

(5) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.

(6) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7315 to clear it?

(7) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.

(8) 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?

(9) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 8% simple interest?

(10) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 8 years.