Simple Interest
Math MCQs

Question :    Barbara had to pay $3763 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  $3550

Solution & Explanation

Solution

Given,

Amount (A) = $3763

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

$3763 = P (1 + 2% × 3)

⇒ $3763 = P (1 + ²/₁₀₀ × 3)

⇒ $3763 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $3763 = P (1 + ⁶/₁₀₀)

⇒ $3763 = P (^{100 + 6}/₁₀₀)

⇒ $3763 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $3763

⇒ P = ³⁷⁶³/_¹⁰⁶/100

⇒ P = 3763 × ¹⁰⁰/₁₀₆

⇒ P = ^{3763 × 100}/₁₀₆

⇒ P = ³⁷⁶³⁰⁰/₁₀₆

⇒ P = $3550

Thus, the sum borrowed (P) = $3550 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 3763, then the Principal = ¹⁰⁰/₁₀₆ × 3763

= ^{100 × 3763}/₁₀₆

= ³⁷⁶³⁰⁰/₁₀₆

= 3550

Thus, Principal = $3550

Thus, the sum borrowed = $3550 Answer

Similar Questions

(1) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7708 to clear the loan, then find the time period of the loan.

(2) Anthony had to pay $4816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(3) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 4% simple interest?

(4) Calculate the amount due if Mary borrowed a sum of $3050 at 7% simple interest for 4 years.

(5) Find the amount to be paid if James borrowed a sum of $5000 at 10% simple interest for 7 years.

(6) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.

(7) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 9% simple interest?

(8) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7897 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Jessica borrowed a sum of $5750 at 2% simple interest for 8 years.

(10) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.