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

(2) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 6% simple interest.

(3) Calculate the amount due if Joseph borrowed a sum of $3700 at 8% simple interest for 4 years.

(4) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 8% simple interest?

(5) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 7% simple interest?

(6) What amount does William have to pay after 5 years if he takes a loan of $3500 at 4% simple interest?

(7) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5775 to clear it?

(8) Robert had to pay $3286 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(9) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.

(10) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.