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) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

(2) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 7% simple interest?

(3) Mark had to pay $4928 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(4) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 4% simple interest.

(5) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 9% simple interest.

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

(7) How much loan did Mark borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7040 to clear it?

(8) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 2% simple interest?

(9) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $10608 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 7 years.