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) If Susan borrowed $3650 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(2) If Joseph borrowed $3700 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(3) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 8% simple interest.

(4) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 8% simple interest?

(5) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 10% simple interest?

(6) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 3% simple interest.

(7) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 8 years.

(8) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.

(9) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.

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