Simple Interest
Math MCQs

Question :    Susan had to pay $3869 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

Correct Answer  $3650

Solution & Explanation

Solution

Given,

Amount (A) = $3869

Rate of Simple Interest (R) = 2%

Time (T) = 3 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

$3869 = P (1 + 2% × 3)

⇒ $3869 = P (1 + ²/₁₀₀ × 3)

⇒ $3869 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $3869 = P (1 + ⁶/₁₀₀)

⇒ $3869 = P (^{100 + 6}/₁₀₀)

⇒ $3869 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $3869

⇒ P = ³⁸⁶⁹/_¹⁰⁶/100

⇒ P = 3869 × ¹⁰⁰/₁₀₆

⇒ P = ^{3869 × 100}/₁₀₆

⇒ P = ³⁸⁶⁹⁰⁰/₁₀₆

⇒ P = $3650

Thus, the sum borrowed (P) = $3650 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 = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 2 = 6

Thus, simple interest for 3 years = 6

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 6 = 106

Calculation of the Principal

Now,

∵ If the Amount is 106, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₆

∴ If the Amount is 3869, then the Principal = ¹⁰⁰/₁₀₆ × 3869

= ^{100 × 3869}/₁₀₆

= ³⁸⁶⁹⁰⁰/₁₀₆

= 3650

Thus, Principal = $3650

Thus, the sum borrowed = $3650 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.

(2) What amount does William have to pay after 5 years if he takes a loan of $3500 at 10% simple interest?

(3) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 4% simple interest?

(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 7 years.

(5) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 4% simple interest?

(6) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.

(7) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12127 to clear the loan, then find the time period of the loan.

(8) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.

(9) If Matthew paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(10) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.