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) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.

(2) What amount will be due after 2 years if John borrowed a sum of $3100 at a 9% simple interest?

(3) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.

(4) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 10% simple interest?

(5) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9310 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 8 years.

(7) In how much time a principal of $3100 will amount to $3410 at a simple interest of 2% per annum?

(8) If Paul paid $5452 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(9) What amount does William have to pay after 5 years if he takes a loan of $3500 at 5% simple interest?

(10) In how much time a principal of $3050 will amount to $3324.5 at a simple interest of 3% per annum?