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) Find the amount to be paid if Linda borrowed a sum of $5350 at 5% simple interest for 8 years.

(2) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.

(4) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.

(5) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6562.5 to clear it?

(6) Calculate the amount due if Joseph borrowed a sum of $3700 at 9% simple interest for 3 years.

(7) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Thomas borrowed a sum of $3800 at 6% simple interest for 4 years.

(9) Robert had to pay $3565 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) In how much time a principal of $3200 will amount to $3680 at a simple interest of 3% per annum?