Simple Interest
Math MCQs

Question :    Elizabeth had to pay $3657 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  $3450

Solution & Explanation

Solution

Given,

Amount (A) = $3657

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

$3657 = P (1 + 2% × 3)

⇒ $3657 = P (1 + ²/₁₀₀ × 3)

⇒ $3657 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $3657 = P (1 + ⁶/₁₀₀)

⇒ $3657 = P (^{100 + 6}/₁₀₀)

⇒ $3657 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $3657

⇒ P = ³⁶⁵⁷/_¹⁰⁶/100

⇒ P = 3657 × ¹⁰⁰/₁₀₆

⇒ P = ^{3657 × 100}/₁₀₆

⇒ P = ³⁶⁵⁷⁰⁰/₁₀₆

⇒ P = $3450

Thus, the sum borrowed (P) = $3450 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 3657, then the Principal = ¹⁰⁰/₁₀₆ × 3657

= ^{100 × 3657}/₁₀₆

= ³⁶⁵⁷⁰⁰/₁₀₆

= 3450

Thus, Principal = $3450

Thus, the sum borrowed = $3450 Answer

Similar Questions

(1) Calculate the amount due if Linda borrowed a sum of $3350 at 8% simple interest for 3 years.

(2) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.

(3) How much loan did Betty borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7500 to clear it?

(4) Calculate the amount due if Charles borrowed a sum of $3900 at 3% simple interest for 3 years.

(5) Margaret had to pay $4611 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) Calculate the amount due if Michael borrowed a sum of $3300 at 4% simple interest for 4 years.

(7) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 3 years.

(9) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 7 years.

(10) If Michael borrowed $3300 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.