Simple Interest
Math MCQs

Question :    Andrew had to pay $5232 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

Correct Answer  $4800

Solution & Explanation

Solution

Given,

Amount (A) = $5232

Rate of Simple Interest (R) = 3%

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

$5232 = P (1 + 3% × 3)

⇒ $5232 = P (1 + ³/₁₀₀ × 3)

⇒ $5232 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $5232 = P (1 + ⁹/₁₀₀)

⇒ $5232 = P (^{100 + 9}/₁₀₀)

⇒ $5232 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $5232

⇒ P = ⁵²³²/_¹⁰⁹/100

⇒ P = 5232 × ¹⁰⁰/₁₀₉

⇒ P = ^{5232 × 100}/₁₀₉

⇒ P = ⁵²³²⁰⁰/₁₀₉

⇒ P = $4800

Thus, the sum borrowed (P) = $4800 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 9

Thus, simple interest for 3 years = 9

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 9 = 109

Calculation of the Principal

Now,

∵ If the Amount is 109, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₉

∴ If the Amount is 5232, then the Principal = ¹⁰⁰/₁₀₉ × 5232

= ^{100 × 5232}/₁₀₉

= ⁵²³²⁰⁰/₁₀₉

= 4800

Thus, Principal = $4800

Thus, the sum borrowed = $4800 Answer

Similar Questions

(1) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.

(2) If Sarah paid $4312 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(3) In how much time a principal of $3000 will amount to $3360 at a simple interest of 4% per annum?

(4) Calculate the amount due if Robert borrowed a sum of $3100 at 2% simple interest for 3 years.

(5) Calculate the amount due if Michael borrowed a sum of $3300 at 3% simple interest for 3 years.

(6) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 9% simple interest.

(7) What amount will be due after 2 years if David borrowed a sum of $3200 at a 7% simple interest?

(8) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 3% simple interest.

(9) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 2% simple interest.

(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 4 years.