Simple Interest
Math MCQs

Question :    Michael had to pay $3795 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

Correct Answer  $3300

Solution & Explanation

Solution

Given,

Amount (A) = $3795

Rate of Simple Interest (R) = 5%

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

$3795 = P (1 + 5% × 3)

⇒ $3795 = P (1 + ⁵/₁₀₀ × 3)

⇒ $3795 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $3795 = P (1 + ¹⁵/₁₀₀)

⇒ $3795 = P (^{100 + 15}/₁₀₀)

⇒ $3795 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $3795

⇒ P = ³⁷⁹⁵/_¹¹⁵/100

⇒ P = 3795 × ¹⁰⁰/₁₁₅

⇒ P = ^{3795 × 100}/₁₁₅

⇒ P = ³⁷⁹⁵⁰⁰/₁₁₅

⇒ 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 15

Thus, simple interest for 3 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 3795, then the Principal = ¹⁰⁰/₁₁₅ × 3795

= ^{100 × 3795}/₁₁₅

= ³⁷⁹⁵⁰⁰/₁₁₅

= 3300

Thus, Principal = $3300

Thus, the sum borrowed = $3300 Answer

Similar Questions

(1) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 3% simple interest?

(2) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.

(3) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 5% simple interest?

(4) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 3 years.

(5) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7450 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 4 years.

(7) How much loan did Mary borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5555 to clear it?

(8) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 2% simple interest.

(9) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 7 years.

(10) If Margaret paid $5046 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.