Simple Interest
MCQs Math


Question:     How much loan did Donald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7475 to clear it?


Correct Answer  $6500

Solution And Explanation

Solution

Given,

Amount (A) = $7475

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

$7475 = P (1 + 3% × 5)

⇒ $7475 = P (1 + 3/100 × 5)

⇒ $7475 = P (1 + 3 × 5/100)

⇒ $7475 = P (1 + 15/100)

⇒ $7475 = P (100 + 15/100)

⇒ $7475 = P × 115/100

⇒ P × 115/100 = $7475

⇒ P = 7475/115/100

⇒ P = 7475 × 100/115

⇒ P = 7475 × 100/115

⇒ P = 747500/115

⇒ P = $6500

Thus, the sum borrowed (P) = $6500 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 7475, then the Principal = 100/115 × 7475

= 100 × 7475/115

= 747500/115

= 6500

Thus, Principal = $6500

Thus, the sum borrowed = $6500 Answer


Similar Questions

(1) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $11880 to clear the loan, then find the time period of the loan.

(2) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 9% simple interest?

(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 3 years.

(4) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 8% simple interest.

(5) Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 7 years.

(6) How much loan did Deborah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8940 to clear it?

(7) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 4 years.

(8) William had to pay $3920 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(9) Calculate the amount due if Jennifer borrowed a sum of $3250 at 5% simple interest for 4 years.

(10) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 4 years.


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