Simple Interest
MCQs Math


Question:     How much loan did Ashley borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7532.5 to clear it?


Correct Answer  $6550

Solution And Explanation

Solution

Given,

Amount (A) = $7532.5

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

$7532.5 = P (1 + 3% × 5)

⇒ $7532.5 = P (1 + 3/100 × 5)

⇒ $7532.5 = P (1 + 3 × 5/100)

⇒ $7532.5 = P (1 + 15/100)

⇒ $7532.5 = P (100 + 15/100)

⇒ $7532.5 = P × 115/100

⇒ P × 115/100 = $7532.5

⇒ P = 7532.5/115/100

⇒ P = 7532.5 × 100/115

⇒ P = 7532.5 × 100/115

⇒ P = 753250/115

⇒ P = $6550

Thus, the sum borrowed (P) = $6550 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 7532.5, then the Principal = 100/115 × 7532.5

= 100 × 7532.5/115

= 753250/115

= 6550

Thus, Principal = $6550

Thus, the sum borrowed = $6550 Answer


Similar Questions

(1) Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 7 years.

(2) If Joseph paid $4440 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(3) How much loan did Anthony borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7560 to clear it?

(4) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 2% simple interest?

(5) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 7 years.

(6) If Mary borrowed $3050 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(7) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.

(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 8% simple interest for 3 years.

(9) Calculate the amount due if Susan borrowed a sum of $3650 at 3% simple interest for 4 years.

(10) How much loan did Barbara borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6937.5 to clear it?


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