Simple Interest
Math MCQs

Question :    Donald had to pay $4905 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  $4500

Solution & Explanation

Solution

Given,

Amount (A) = $4905

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

$4905 = P (1 + 3% × 3)

⇒ $4905 = P (1 + ³/₁₀₀ × 3)

⇒ $4905 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $4905 = P (1 + ⁹/₁₀₀)

⇒ $4905 = P (^{100 + 9}/₁₀₀)

⇒ $4905 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $4905

⇒ P = ⁴⁹⁰⁵/_¹⁰⁹/100

⇒ P = 4905 × ¹⁰⁰/₁₀₉

⇒ P = ^{4905 × 100}/₁₀₉

⇒ P = ⁴⁹⁰⁵⁰⁰/₁₀₉

⇒ P = $4500

Thus, the sum borrowed (P) = $4500 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 4905, then the Principal = ¹⁰⁰/₁₀₉ × 4905

= ^{100 × 4905}/₁₀₉

= ⁴⁹⁰⁵⁰⁰/₁₀₉

= 4500

Thus, Principal = $4500

Thus, the sum borrowed = $4500 Answer

Similar Questions

(1) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $11247 to clear the loan, then find the time period of the loan.

(2) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 4% simple interest?

(3) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 4% simple interest?

(4) How much loan did Margaret borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7937.5 to clear it?

(5) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 7% simple interest.

(6) Michelle had to pay $5544 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 4 years.

(8) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Susan borrowed a sum of $3650 at 2% simple interest for 4 years.

(10) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 4% simple interest?