Simple Interest
Math MCQs

Question :    How much loan did Michael borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6095 to clear it?

Correct Answer  $5300

Solution & Explanation

Solution

Given,

Amount (A) = $6095

Rate of Simple Interest (R) = 3%

Time (T) = 5 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

$6095 = P (1 + 3% × 5)

⇒ $6095 = P (1 + ³/₁₀₀ × 5)

⇒ $6095 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $6095 = P (1 + ¹⁵/₁₀₀)

⇒ $6095 = P (^{100 + 15}/₁₀₀)

⇒ $6095 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $6095

⇒ P = ⁶⁰⁹⁵/_¹¹⁵/100

⇒ P = 6095 × ¹⁰⁰/₁₁₅

⇒ P = ^{6095 × 100}/₁₁₅

⇒ P = ⁶⁰⁹⁵⁰⁰/₁₁₅

⇒ P = $5300

Thus, the sum borrowed (P) = $5300 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 = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 3 = 15

Thus, simple interest for 5 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 6095, then the Principal = ¹⁰⁰/₁₁₅ × 6095

= ^{100 × 6095}/₁₁₅

= ⁶⁰⁹⁵⁰⁰/₁₁₅

= 5300

Thus, Principal = $5300

Thus, the sum borrowed = $5300 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.

(2) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 9% simple interest.

(3) Calculate the amount due if Michael borrowed a sum of $3300 at 2% simple interest for 3 years.

(4) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7964 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if David borrowed a sum of $5400 at 6% simple interest for 8 years.

(6) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 7% simple interest?

(7) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 8 years.

(8) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 2% simple interest for 4 years.

(10) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 3 years.