Simple Interest
Math MCQs

Question :    Karen had to pay $4305.5 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  $3950

Solution & Explanation

Solution

Given,

Amount (A) = $4305.5

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

$4305.5 = P (1 + 3% × 3)

⇒ $4305.5 = P (1 + ³/₁₀₀ × 3)

⇒ $4305.5 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $4305.5 = P (1 + ⁹/₁₀₀)

⇒ $4305.5 = P (^{100 + 9}/₁₀₀)

⇒ $4305.5 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $4305.5

⇒ P = ^4305.5/_¹⁰⁹/100

⇒ P = 4305.5 × ¹⁰⁰/₁₀₉

⇒ P = ^{4305.5 × 100}/₁₀₉

⇒ P = ⁴³⁰⁵⁵⁰/₁₀₉

⇒ P = $3950

Thus, the sum borrowed (P) = $3950 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 4305.5, then the Principal = ¹⁰⁰/₁₀₉ × 4305.5

= ^{100 × 4305.5}/₁₀₉

= ⁴³⁰⁵⁵⁰/₁₀₉

= 3950

Thus, Principal = $3950

Thus, the sum borrowed = $3950 Answer

Similar Questions

(1) If Karen paid $4740 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(2) How much loan did Jacob borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8800 to clear it?

(3) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $11000 to clear the loan, then find the time period of the loan.

(4) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 6% simple interest?

(5) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 9% simple interest.

(6) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 8% simple interest?

(7) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.

(8) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 4 years.

(9) In how much time a principal of $3050 will amount to $3233 at a simple interest of 2% per annum?

(10) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.