Simple Interest
Math MCQs

Question :    If Jessica paid $4050 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $3750

Solution & Explanation

Solution

Given,

Amount (A) = $4050

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

$4050 = P (1 + 2% × 4)

⇒ $4050 = P (1 + ²/₁₀₀ × 4)

⇒ $4050 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $4050 = P (1 + ⁸/₁₀₀)

⇒ $4050 = P (^{100 + 8}/₁₀₀)

⇒ $4050 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $4050

⇒ P = ⁴⁰⁵⁰/_¹⁰⁸/100

⇒ P = 4050 × ¹⁰⁰/₁₀₈

⇒ P = ^{4050 × 100}/₁₀₈

⇒ P = ⁴⁰⁵⁰⁰⁰/₁₀₈

⇒ P = $3750

Thus, the sum borrowed (P) = $3750 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 4050, then the Principal = ¹⁰⁰/₁₀₈ × 4050

= ^{100 × 4050}/₁₀₈

= ⁴⁰⁵⁰⁰⁰/₁₀₈

= 3750

Thus, Principal = $3750

Thus, the sum borrowed = $3750 Answer

Similar Questions

(1) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 9% simple interest for 7 years.

(3) In how much time a principal of $3200 will amount to $3328 at a simple interest of 2% per annum?

(4) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 8% simple interest?

(5) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.

(6) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.

(7) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 3 years.

(9) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.

(10) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.