Simple Interest
Math MCQs

Question :    Margaret had to pay $4741.5 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  $4350

Solution & Explanation

Solution

Given,

Amount (A) = $4741.5

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

$4741.5 = P (1 + 3% × 3)

⇒ $4741.5 = P (1 + ³/₁₀₀ × 3)

⇒ $4741.5 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $4741.5 = P (1 + ⁹/₁₀₀)

⇒ $4741.5 = P (^{100 + 9}/₁₀₀)

⇒ $4741.5 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $4741.5

⇒ P = ^4741.5/_¹⁰⁹/100

⇒ P = 4741.5 × ¹⁰⁰/₁₀₉

⇒ P = ^{4741.5 × 100}/₁₀₉

⇒ P = ⁴⁷⁴¹⁵⁰/₁₀₉

⇒ P = $4350

Thus, the sum borrowed (P) = $4350 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 4741.5, then the Principal = ¹⁰⁰/₁₀₉ × 4741.5

= ^{100 × 4741.5}/₁₀₉

= ⁴⁷⁴¹⁵⁰/₁₀₉

= 4350

Thus, Principal = $4350

Thus, the sum borrowed = $4350 Answer

Similar Questions

(1) Find the amount to be paid if John borrowed a sum of $5200 at 8% simple interest for 8 years.

(2) What amount does William have to pay after 5 years if he takes a loan of $3500 at 3% simple interest?

(3) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 8% simple interest?

(4) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 10% simple interest?

(5) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 10% simple interest?

(6) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 9% simple interest.

(7) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 3% simple interest?

(8) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 3% simple interest?

(9) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.

(10) If Richard borrowed $3600 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.