Simple Interest
Math MCQs

Question :    If Jessica paid $4350 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $3750

Solution & Explanation

Solution

Given,

Amount (A) = $4350

Rate of Simple Interest (R) = 4%

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

$4350 = P (1 + 4% × 4)

⇒ $4350 = P (1 + ⁴/₁₀₀ × 4)

⇒ $4350 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $4350 = P (1 + ¹⁶/₁₀₀)

⇒ $4350 = P (^{100 + 16}/₁₀₀)

⇒ $4350 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $4350

⇒ P = ⁴³⁵⁰/_¹¹⁶/100

⇒ P = 4350 × ¹⁰⁰/₁₁₆

⇒ P = ^{4350 × 100}/₁₁₆

⇒ P = ⁴³⁵⁰⁰⁰/₁₁₆

⇒ 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 16

Thus, simple interest for 4 years = 16

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 16 = 116

Calculation of the Principal

Now,

∵ If the Amount is 116, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₆

∴ If the Amount is 4350, then the Principal = ¹⁰⁰/₁₁₆ × 4350

= ^{100 × 4350}/₁₁₆

= ⁴³⁵⁰⁰⁰/₁₁₆

= 3750

Thus, Principal = $3750

Thus, the sum borrowed = $3750 Answer

Similar Questions

(1) How much loan did Jason borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8470 to clear it?

(2) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 9% simple interest for 3 years.

(4) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 10% simple interest?

(5) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 4% simple interest?

(6) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.

(7) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 5% simple interest?

(8) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 3 years.

(10) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.