Simple Interest
Math MCQs

Question :    Michael had to pay $3597 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  $3300

Solution & Explanation

Solution

Given,

Amount (A) = $3597

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

$3597 = P (1 + 3% × 3)

⇒ $3597 = P (1 + ³/₁₀₀ × 3)

⇒ $3597 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $3597 = P (1 + ⁹/₁₀₀)

⇒ $3597 = P (^{100 + 9}/₁₀₀)

⇒ $3597 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $3597

⇒ P = ³⁵⁹⁷/_¹⁰⁹/100

⇒ P = 3597 × ¹⁰⁰/₁₀₉

⇒ P = ^{3597 × 100}/₁₀₉

⇒ P = ³⁵⁹⁷⁰⁰/₁₀₉

⇒ P = $3300

Thus, the sum borrowed (P) = $3300 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 3597, then the Principal = ¹⁰⁰/₁₀₉ × 3597

= ^{100 × 3597}/₁₀₉

= ³⁵⁹⁷⁰⁰/₁₀₉

= 3300

Thus, Principal = $3300

Thus, the sum borrowed = $3300 Answer

Similar Questions

(1) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9840 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Jessica borrowed a sum of $3750 at 2% simple interest for 3 years.

(3) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.

(4) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 7% simple interest?

(5) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 7 years.

(6) Kimberly had to pay $5068.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(7) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.

(8) Sarah had to pay $4427.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(9) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.

(10) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.