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Simple Interest
Math MCQs


Question :    How much loan did Betty borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7812.5 to clear it?


Correct Answer  $6250

Solution & Explanation

Solution

Given,

Amount (A) = $7812.5

Rate of Simple Interest (R) = 5%

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

$7812.5 = P (1 + 5% × 5)

⇒ $7812.5 = P (1 + 5/100 × 5)

⇒ $7812.5 = P (1 + 5 × 5/100)

⇒ $7812.5 = P (1 + 25/100)

⇒ $7812.5 = P (100 + 25/100)

⇒ $7812.5 = P × 125/100

⇒ P × 125/100 = $7812.5

⇒ P = 7812.5/125/100

⇒ P = 7812.5 × 100/125

⇒ P = 7812.5 × 100/125

⇒ P = 781250/125

⇒ P = $6250

Thus, the sum borrowed (P) = $6250 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = 100/125

∴ If the Amount is 7812.5, then the Principal = 100/125 × 7812.5

= 100 × 7812.5/125

= 781250/125

= 6250

Thus, Principal = $6250

Thus, the sum borrowed = $6250 Answer


Similar Questions

(1) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 5% per annum?

(2) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.

(3) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.

(4) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10132 to clear the loan, then find the time period of the loan.

(5) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.

(6) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 3% simple interest.

(8) Jennifer had to pay $3542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(9) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.

(10) If Jennifer paid $3900 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.