Simple Interest
Math MCQs

Question :    How much loan did Joseph borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6555 to clear it?

Correct Answer  $5700

Solution & Explanation

Solution

Given,

Amount (A) = $6555

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

$6555 = P (1 + 3% × 5)

⇒ $6555 = P (1 + ³/₁₀₀ × 5)

⇒ $6555 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $6555 = P (1 + ¹⁵/₁₀₀)

⇒ $6555 = P (^{100 + 15}/₁₀₀)

⇒ $6555 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $6555

⇒ P = ⁶⁵⁵⁵/_¹¹⁵/100

⇒ P = 6555 × ¹⁰⁰/₁₁₅

⇒ P = ^{6555 × 100}/₁₁₅

⇒ P = ⁶⁵⁵⁵⁰⁰/₁₁₅

⇒ P = $5700

Thus, the sum borrowed (P) = $5700 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 6555, then the Principal = ¹⁰⁰/₁₁₅ × 6555

= ^{100 × 6555}/₁₁₅

= ⁶⁵⁵⁵⁰⁰/₁₁₅

= 5700

Thus, Principal = $5700

Thus, the sum borrowed = $5700 Answer

Similar Questions

(1) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 7% simple interest.

(2) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.

(3) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12800 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 3 years.

(5) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.

(6) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6240 to clear the loan, then find the time period of the loan.

(7) Richard had to pay $3816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

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

(9) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8820 to clear the loan, then find the time period of the loan.

(10) How much loan did Brian borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8640 to clear it?