Simple Interest
MCQs Math


Question:     In how much time a principal of $3100 will amount to $3565 at a simple interest of 5% per annum?


Correct Answer  3

Solution And Explanation

Solution

Given,

Principal (P) = $3100

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

Amount (A) = $3565

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 = $3565 – $3100 = $465

Thus, Simple Interest = $465

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 × 465/3100 × 5

= 46500/15500

= 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) = $3100

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

Simple Interest = $465 (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 $3100

= 5/100 × 3100

= 5 × 3100/100

= 15500/100 = 155

Thus, simple Interest for 1 year = $155

Now,

∵ If the simple Interest is $155, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/155 years

∴ If the simple Interest is $465, then the time = 1/155 × 465 years

= 1 × 465/155 years

= 465/155 = 3 years

Thus, time (T) = 3 years Answer


Similar Questions

(1) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 8% simple interest?

(2) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 2% simple interest.

(3) Find the amount to be paid if John borrowed a sum of $5200 at 4% simple interest for 7 years.

(4) If Ashley paid $4914 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(5) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 7 years.

(6) Calculate the amount due if Karen borrowed a sum of $3950 at 7% simple interest for 4 years.

(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 7 years.

(8) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.

(9) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 3% simple interest?

(10) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 5% simple interest?


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