Simple Interest
Math MCQs

Question :    If John paid $3840 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $3200

Solution & Explanation

Solution

Given,

Amount (A) = $3840

Rate of Simple Interest (R) = 5%

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

$3840 = P (1 + 5% × 4)

⇒ $3840 = P (1 + ⁵/₁₀₀ × 4)

⇒ $3840 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $3840 = P (1 + ²⁰/₁₀₀)

⇒ $3840 = P (^{100 + 20}/₁₀₀)

⇒ $3840 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $3840

⇒ P = ³⁸⁴⁰/_¹²⁰/100

⇒ P = 3840 × ¹⁰⁰/₁₂₀

⇒ P = ^{3840 × 100}/₁₂₀

⇒ P = ³⁸⁴⁰⁰⁰/₁₂₀

⇒ P = $3200

Thus, the sum borrowed (P) = $3200 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 20

Thus, simple interest for 4 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 3840, then the Principal = ¹⁰⁰/₁₂₀ × 3840

= ^{100 × 3840}/₁₂₀

= ³⁸⁴⁰⁰⁰/₁₂₀

= 3200

Thus, Principal = $3200

Thus, the sum borrowed = $3200 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 6% simple interest.

(2) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.

(3) If Sandra paid $5340 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(4) Daniel had to pay $4715 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(5) How much loan did Michelle borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7645 to clear it?

(6) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 6% simple interest.

(7) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 10% simple interest.

(8) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $9010 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 4% simple interest.

(10) Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 7 years.