Simple Interest
Math MCQs

Question :    Christopher had to pay $4480 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

Correct Answer  $4000

Solution & Explanation

Solution

Given,

Amount (A) = $4480

Rate of Simple Interest (R) = 4%

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

$4480 = P (1 + 4% × 3)

⇒ $4480 = P (1 + ⁴/₁₀₀ × 3)

⇒ $4480 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $4480 = P (1 + ¹²/₁₀₀)

⇒ $4480 = P (^{100 + 12}/₁₀₀)

⇒ $4480 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4480

⇒ P = ⁴⁴⁸⁰/_¹¹²/100

⇒ P = 4480 × ¹⁰⁰/₁₁₂

⇒ P = ^{4480 × 100}/₁₁₂

⇒ P = ⁴⁴⁸⁰⁰⁰/₁₁₂

⇒ P = $4000

Thus, the sum borrowed (P) = $4000 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 12

Thus, simple interest for 3 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₂

∴ If the Amount is 4480, then the Principal = ¹⁰⁰/₁₁₂ × 4480

= ^{100 × 4480}/₁₁₂

= ⁴⁴⁸⁰⁰⁰/₁₁₂

= 4000

Thus, Principal = $4000

Thus, the sum borrowed = $4000 Answer

Similar Questions

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

(2) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.

(3) Calculate the amount due if Jessica borrowed a sum of $3750 at 7% simple interest for 3 years.

(4) 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.

(5) How much loan did Margaret borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7302.5 to clear it?

(6) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 4% simple interest?

(7) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.

(9) Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 7 years.

(10) How much loan did Barbara borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6105 to clear it?