Simple Interest
MCQs Math


Question:     Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7544 to clear the loan, then find the time period of the loan.


Correct Answer  8

Solution And Explanation

Solution

Given,

Principal (P) = $4600

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $7544

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 = $7544 – $4600 = $2944

Thus, Simple Interest = $2944

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 × 2944/4600 × 8

= 294400/36800

= 8 years (using formula)

Thus, Time (T) = 8 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) = $4600

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $2944 (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 = 8% of Principal

= 8% of $4600

= 8/100 × 4600

= 8 × 4600/100

= 36800/100 = 368

Thus, simple Interest for 1 year = $368

Now,

∵ If the simple Interest is $368, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/368 years

∴ If the simple Interest is $2944, then the time = 1/368 × 2944 years

= 1 × 2944/368 years

= 2944/368 = 8 years

Thus, time (T) = 8 years Answer


Similar Questions

(1) How much loan did Matthew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6820 to clear it?

(2) If Kenneth paid $6000 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(3) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 8% simple interest?

(4) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 8% simple interest?

(5) Find the amount to be paid if Barbara borrowed a sum of $5550 at 8% simple interest for 7 years.

(6) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 8 years.

(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 9% simple interest for 4 years.

(8) What amount does John have to pay after 6 years if he takes a loan of $3200 at 8% simple interest?

(9) How much loan did Sarah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6435 to clear it?

(10) In how much time a principal of $3200 will amount to $3584 at a simple interest of 3% per annum?


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