Simple Interest
MCQs Math


Question:     In how much time a principal of $3000 will amount to $3750 at a simple interest of 5% per annum?


Correct Answer  5

Solution And Explanation

Solution

Given,

Principal (P) = $3000

Rate of Simple Interest (R) = 5% per annum

Amount (A) = $3750

Thus, time (T) = ?

Method (1) Using Formula

Calculation of Simple Interest, when Principal and Amount are given

Formual to Calculate Simple Interest when Principal and Amount are given

We know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $3750 – $3000 = $750

Thus, Simple Interest = $750

Calculation of the Time using forumula when Amount, Simple Interest and Principal are known

Formula to find the Time (T)

Time (T) = 100 × Simple Interest/Principal × Rate of Interest

⇒ T = 100 × SI/P × R

Thus, Time (T) = 100 × 750/3000 × 5

= 75000/15000

= 5 years (using formula)

Thus, Time (T) = 5 years (from time taken before calculation)Answer

Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known

Here, we have

Principal (P) = $3000

Rate of Simple Interest (R) = 5% per annum

Simple Interest = $750 (As calculated above by subtracting Principal from the Amount given)

We know that, interest is calculated on the basis of the Principal.

This means Simple Interest for 1 year = Rate of simple interest × Principal

Thus, Simple Interest for 1 year = 5% of Principal

= 5% of $3000

= 5/100 × 3000

= 5 × 3000/100

= 15000/100 = 150

Thus, simple Interest for 1 year = $150

Now,

∵ If the simple Interest is $150, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/150 years

∴ If the simple Interest is $750, then the time = 1/150 × 750 years

= 1 × 750/150 years

= 750/150 = 5 years

Thus, time (T) = 5 years Answer


Similar Questions

(1) Calculate the amount due if Patricia borrowed a sum of $3150 at 10% simple interest for 3 years.

(2) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 5% simple interest.

(3) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.

(4) In how much time a principal of $3000 will amount to $3240 at a simple interest of 4% per annum?

(5) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 7 years.

(7) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 7% simple interest?

(8) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 7% simple interest?

(9) Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 8 years.

(10) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 8% simple interest?


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