Simple Interest
MCQs Math


Question:     In how much time a principal of $3050 will amount to $3233 at a simple interest of 2% per annum?


Correct Answer  3

Solution And Explanation

Solution

Given,

Principal (P) = $3050

Rate of Simple Interest (R) = 2% per annum

Amount (A) = $3233

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 = $3233 – $3050 = $183

Thus, Simple Interest = $183

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 × 183/3050 × 2

= 18300/6100

= 3 years (using formula)

Thus, Time (T) = 3 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) = $3050

Rate of Simple Interest (R) = 2% per annum

Simple Interest = $183 (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 = 2% of Principal

= 2% of $3050

= 2/100 × 3050

= 2 × 3050/100

= 6100/100 = 61

Thus, simple Interest for 1 year = $61

Now,

∵ If the simple Interest is $61, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/61 years

∴ If the simple Interest is $183, then the time = 1/61 × 183 years

= 1 × 183/61 years

= 183/61 = 3 years

Thus, time (T) = 3 years Answer


Similar Questions

(1) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.

(2) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6068 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 5% simple interest.

(4) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 2% simple interest?

(5) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 6% simple interest?

(6) Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 3 years.

(7) What amount does James have to pay after 6 years if he takes a loan of $3000 at 4% simple interest?

(8) If Matthew paid $4704 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(9) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8140 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 8 years.


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