Simple Interest
Math MCQs

Question :    Sarah had to pay $4081 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  $3850

Solution & Explanation

Solution

Given,

Amount (A) = $4081

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

$4081 = P (1 + 2% × 3)

⇒ $4081 = P (1 + ²/₁₀₀ × 3)

⇒ $4081 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $4081 = P (1 + ⁶/₁₀₀)

⇒ $4081 = P (^{100 + 6}/₁₀₀)

⇒ $4081 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $4081

⇒ P = ⁴⁰⁸¹/_¹⁰⁶/100

⇒ P = 4081 × ¹⁰⁰/₁₀₆

⇒ P = ^{4081 × 100}/₁₀₆

⇒ P = ⁴⁰⁸¹⁰⁰/₁₀₆

⇒ P = $3850

Thus, the sum borrowed (P) = $3850 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 4081, then the Principal = ¹⁰⁰/₁₀₆ × 4081

= ^{100 × 4081}/₁₀₆

= ⁴⁰⁸¹⁰⁰/₁₀₆

= 3850

Thus, Principal = $3850

Thus, the sum borrowed = $3850 Answer

Similar Questions

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

(2) How much loan did John borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6240 to clear it?

(3) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 9% simple interest?

(4) What amount will be due after 2 years if William borrowed a sum of $3250 at a 9% simple interest?

(5) What amount does John have to pay after 5 years if he takes a loan of $3200 at 10% simple interest?

(6) Calculate the amount due if Patricia borrowed a sum of $3150 at 7% simple interest for 4 years.

(7) How much loan did Ronald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9000 to clear it?

(8) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 9% simple interest for 8 years.

(10) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8493 to clear the loan, then find the time period of the loan.