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) How much loan did Jason borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8470 to clear it?

(2) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 2% simple interest.

(3) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 3% simple interest?

(4) Calculate the amount due if Linda borrowed a sum of $3350 at 8% simple interest for 3 years.

(5) Mary had to pay $3416 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(6) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 4 years.

(7) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 8 years.

(9) Steven had to pay $5014 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(10) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.