Simple Interest
Math MCQs

Question :    If Elizabeth paid $3726 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $3450

Solution & Explanation

Solution

Given,

Amount (A) = $3726

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

$3726 = P (1 + 2% × 4)

⇒ $3726 = P (1 + ²/₁₀₀ × 4)

⇒ $3726 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $3726 = P (1 + ⁸/₁₀₀)

⇒ $3726 = P (^{100 + 8}/₁₀₀)

⇒ $3726 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $3726

⇒ P = ³⁷²⁶/_¹⁰⁸/100

⇒ P = 3726 × ¹⁰⁰/₁₀₈

⇒ P = ^{3726 × 100}/₁₀₈

⇒ P = ³⁷²⁶⁰⁰/₁₀₈

⇒ P = $3450

Thus, the sum borrowed (P) = $3450 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 3726, then the Principal = ¹⁰⁰/₁₀₈ × 3726

= ^{100 × 3726}/₁₀₈

= ³⁷²⁶⁰⁰/₁₀₈

= 3450

Thus, Principal = $3450

Thus, the sum borrowed = $3450 Answer

Similar Questions

(1) Calculate the amount due if Richard borrowed a sum of $3600 at 9% simple interest for 3 years.

(2) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9943 to clear the loan, then find the time period of the loan.

(3) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8520 to clear the loan, then find the time period of the loan.

(4) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7242 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.

(6) How much loan did Emily borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7425 to clear it?

(7) Find the amount to be paid if Jessica borrowed a sum of $5750 at 7% simple interest for 7 years.

(8) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 7 years.

(10) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.