Simple Interest
Math MCQs

Question :    Mark had to pay $4796 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  $4400

Solution & Explanation

Solution

Given,

Amount (A) = $4796

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

$4796 = P (1 + 3% × 3)

⇒ $4796 = P (1 + ³/₁₀₀ × 3)

⇒ $4796 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $4796 = P (1 + ⁹/₁₀₀)

⇒ $4796 = P (^{100 + 9}/₁₀₀)

⇒ $4796 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $4796

⇒ P = ⁴⁷⁹⁶/_¹⁰⁹/100

⇒ P = 4796 × ¹⁰⁰/₁₀₉

⇒ P = ^{4796 × 100}/₁₀₉

⇒ P = ⁴⁷⁹⁶⁰⁰/₁₀₉

⇒ P = $4400

Thus, the sum borrowed (P) = $4400 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 4796, then the Principal = ¹⁰⁰/₁₀₉ × 4796

= ^{100 × 4796}/₁₀₉

= ⁴⁷⁹⁶⁰⁰/₁₀₉

= 4400

Thus, Principal = $4400

Thus, the sum borrowed = $4400 Answer

Similar Questions

(1) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 10% simple interest?

(2) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12800 to clear the loan, then find the time period of the loan.

(3) If Daniel paid $4756 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(4) What amount does David have to pay after 5 years if he takes a loan of $3400 at 10% simple interest?

(5) Calculate the amount due if Michael borrowed a sum of $3300 at 10% simple interest for 4 years.

(6) Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 8 years.

(7) Calculate the amount due if James borrowed a sum of $3000 at 2% simple interest for 4 years.

(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 8 years.

(9) How much loan did Andrew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7480 to clear it?

(10) Lisa had to pay $4293 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.