Simple Interest
Math MCQs

Question :    Matthew had to pay $4578 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  $4200

Solution & Explanation

Solution

Given,

Amount (A) = $4578

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

$4578 = P (1 + 3% × 3)

⇒ $4578 = P (1 + ³/₁₀₀ × 3)

⇒ $4578 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $4578 = P (1 + ⁹/₁₀₀)

⇒ $4578 = P (^{100 + 9}/₁₀₀)

⇒ $4578 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $4578

⇒ P = ⁴⁵⁷⁸/_¹⁰⁹/100

⇒ P = 4578 × ¹⁰⁰/₁₀₉

⇒ P = ^{4578 × 100}/₁₀₉

⇒ P = ⁴⁵⁷⁸⁰⁰/₁₀₉

⇒ P = $4200

Thus, the sum borrowed (P) = $4200 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 4578, then the Principal = ¹⁰⁰/₁₀₉ × 4578

= ^{100 × 4578}/₁₀₉

= ⁴⁵⁷⁸⁰⁰/₁₀₉

= 4200

Thus, Principal = $4200

Thus, the sum borrowed = $4200 Answer

Similar Questions

(1) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.

(2) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.

(3) David had to pay $3706 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(4) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 10% simple interest?

(5) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8682.5 to clear it?

(6) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 4% simple interest?

(7) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $10780 to clear the loan, then find the time period of the loan.

(8) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 3 years.

(10) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 7% simple interest.