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Simple Interest
Math MCQs


Question :    Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.


Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $4600

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $8280

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 = $8280 – $4600 = $3680

Thus, Simple Interest = $3680

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 × 3680/4600 × 10

= 368000/46000

= 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) = 10% per annum

Simple Interest = $3680 (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 = 10% of Principal

= 10% of $4600

= 10/100 × 4600

= 10 × 4600/100

= 46000/100 = 460

Thus, simple Interest for 1 year = $460

Now,

∵ If the simple Interest is $460, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/460 years

∴ If the simple Interest is $3680, then the time = 1/460 × 3680 years

= 1 × 3680/460 years

= 3680/460 = 8 years

Thus, time (T) = 8 years Answer


Similar Questions

(1) Find the amount to be paid if Michael borrowed a sum of $5300 at 10% simple interest for 7 years.

(2) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $11000 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 7 years.

(4) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 10% simple interest.

(5) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.

(6) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 2% simple interest.

(7) Calculate the amount due if Linda borrowed a sum of $3350 at 10% simple interest for 3 years.

(8) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.

(9) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 9% simple interest?

(10) Michael had to pay $3498 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.