Simple Interest
Math MCQs

Question :    Jennifer had to pay $3640 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  $3250

Solution & Explanation

Solution

Given,

Amount (A) = $3640

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

$3640 = P (1 + 4% × 3)

⇒ $3640 = P (1 + ⁴/₁₀₀ × 3)

⇒ $3640 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $3640 = P (1 + ¹²/₁₀₀)

⇒ $3640 = P (^{100 + 12}/₁₀₀)

⇒ $3640 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $3640

⇒ P = ³⁶⁴⁰/_¹¹²/100

⇒ P = 3640 × ¹⁰⁰/₁₁₂

⇒ P = ^{3640 × 100}/₁₁₂

⇒ P = ³⁶⁴⁰⁰⁰/₁₁₂

⇒ P = $3250

Thus, the sum borrowed (P) = $3250 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 3640, then the Principal = ¹⁰⁰/₁₁₂ × 3640

= ^{100 × 3640}/₁₁₂

= ³⁶⁴⁰⁰⁰/₁₁₂

= 3250

Thus, Principal = $3250

Thus, the sum borrowed = $3250 Answer

Similar Questions

(1) 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.

(2) What amount does John have to pay after 5 years if he takes a loan of $3200 at 7% simple interest?

(3) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8528 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 7 years.

(5) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 2% simple interest?

(6) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.

(8) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 4 years.

(10) What amount does John have to pay after 5 years if he takes a loan of $3200 at 3% simple interest?