Simple Interest
Math MCQs

Question :    Lisa had to pay $4414.5 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  $4050

Solution & Explanation

Solution

Given,

Amount (A) = $4414.5

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

$4414.5 = P (1 + 3% × 3)

⇒ $4414.5 = P (1 + ³/₁₀₀ × 3)

⇒ $4414.5 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $4414.5 = P (1 + ⁹/₁₀₀)

⇒ $4414.5 = P (^{100 + 9}/₁₀₀)

⇒ $4414.5 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $4414.5

⇒ P = ^4414.5/_¹⁰⁹/100

⇒ P = 4414.5 × ¹⁰⁰/₁₀₉

⇒ P = ^{4414.5 × 100}/₁₀₉

⇒ P = ⁴⁴¹⁴⁵⁰/₁₀₉

⇒ P = $4050

Thus, the sum borrowed (P) = $4050 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 4414.5, then the Principal = ¹⁰⁰/₁₀₉ × 4414.5

= ^{100 × 4414.5}/₁₀₉

= ⁴⁴¹⁴⁵⁰/₁₀₉

= 4050

Thus, Principal = $4050

Thus, the sum borrowed = $4050 Answer

Similar Questions

(1) What amount does James have to pay after 6 years if he takes a loan of $3000 at 6% simple interest?

(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 8% simple interest for 4 years.

(3) How much loan did Anthony borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6930 to clear it?

(4) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 8 years.

(6) Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 7 years.

(7) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.

(8) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 6% simple interest?

(9) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.

(10) If James borrowed $3000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.