Simple Interest
Math MCQs

Question :    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.

Correct Answer  $4350

Solution & Explanation

Solution

Given,

Amount (A) = $4611

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

$4611 = P (1 + 2% × 3)

⇒ $4611 = P (1 + ²/₁₀₀ × 3)

⇒ $4611 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $4611 = P (1 + ⁶/₁₀₀)

⇒ $4611 = P (^{100 + 6}/₁₀₀)

⇒ $4611 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $4611

⇒ P = ⁴⁶¹¹/_¹⁰⁶/100

⇒ P = 4611 × ¹⁰⁰/₁₀₆

⇒ P = ^{4611 × 100}/₁₀₆

⇒ P = ⁴⁶¹¹⁰⁰/₁₀₆

⇒ P = $4350

Thus, the sum borrowed (P) = $4350 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 4611, then the Principal = ¹⁰⁰/₁₀₆ × 4611

= ^{100 × 4611}/₁₀₆

= ⁴⁶¹¹⁰⁰/₁₀₆

= 4350

Thus, Principal = $4350

Thus, the sum borrowed = $4350 Answer

Similar Questions

(1) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 8% simple interest?

(2) Calculate the amount due if Jennifer borrowed a sum of $3250 at 5% simple interest for 3 years.

(3) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.

(4) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.

(5) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.

(6) How much loan did Paul borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7705 to clear it?

(7) Richard had to pay $4032 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(8) Calculate the amount due if John borrowed a sum of $3200 at 3% simple interest for 4 years.

(9) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 6% simple interest.

(10) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 8 years.