Simple Interest
MCQs Math


Question:     How much loan did Amanda borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8222.5 to clear it?


Correct Answer  $7150

Solution And Explanation

Solution

Given,

Amount (A) = $8222.5

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

$8222.5 = P (1 + 3% × 5)

⇒ $8222.5 = P (1 + 3/100 × 5)

⇒ $8222.5 = P (1 + 3 × 5/100)

⇒ $8222.5 = P (1 + 15/100)

⇒ $8222.5 = P (100 + 15/100)

⇒ $8222.5 = P × 115/100

⇒ P × 115/100 = $8222.5

⇒ P = 8222.5/115/100

⇒ P = 8222.5 × 100/115

⇒ P = 8222.5 × 100/115

⇒ P = 822250/115

⇒ P = $7150

Thus, the sum borrowed (P) = $7150 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 8222.5, then the Principal = 100/115 × 8222.5

= 100 × 8222.5/115

= 822250/115

= 7150

Thus, Principal = $7150

Thus, the sum borrowed = $7150 Answer


Similar Questions

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

(2) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 7% simple interest?

(3) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 5% simple interest?

(4) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 5% simple interest?

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

(6) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.

(7) Calculate the amount due if Jennifer borrowed a sum of $3250 at 9% simple interest for 3 years.

(8) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 2% simple interest.

(9) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.

(10) How much loan did Andrew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8160 to clear it?


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