Simple Interest
Math MCQs

Question :    If James paid $3480 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $3000

Solution & Explanation

Solution

Given,

Amount (A) = $3480

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

$3480 = P (1 + 4% × 4)

⇒ $3480 = P (1 + ⁴/₁₀₀ × 4)

⇒ $3480 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $3480 = P (1 + ¹⁶/₁₀₀)

⇒ $3480 = P (^{100 + 16}/₁₀₀)

⇒ $3480 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $3480

⇒ P = ³⁴⁸⁰/_¹¹⁶/100

⇒ P = 3480 × ¹⁰⁰/₁₁₆

⇒ P = ^{3480 × 100}/₁₁₆

⇒ P = ³⁴⁸⁰⁰⁰/₁₁₆

⇒ P = $3000

Thus, the sum borrowed (P) = $3000 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 3480, then the Principal = ¹⁰⁰/₁₁₆ × 3480

= ^{100 × 3480}/₁₁₆

= ³⁴⁸⁰⁰⁰/₁₁₆

= 3000

Thus, Principal = $3000

Thus, the sum borrowed = $3000 Answer

Similar Questions

(1) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.

(3) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Mary borrowed a sum of $3050 at 3% simple interest for 4 years.

(5) Sandra had to pay $4717 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.

(7) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 10% simple interest?

(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 8 years.

(9) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if James borrowed a sum of $3000 at 8% simple interest for 4 years.