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) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 7 years.

(2) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8036 to clear the loan, then find the time period of the loan.

(3) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 6% simple interest?

(4) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 2% simple interest for 7 years.

(6) In how much time a principal of $3000 will amount to $3480 at a simple interest of 4% per annum?

(7) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.

(8) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 10% simple interest?

(9) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 5% simple interest?

(10) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.