Question:
In how much time a principal of $3050 will amount to $3294 at a simple interest of 2% per annum?
Correct Answer
4
Solution And Explanation
Solution
Given,
Principal (P) = $3050
Rate of Simple Interest (R) = 2% per annum
Amount (A) = $3294
Thus, time (T) = ?
Method (1) Using Formula
Calculation of Simple Interest, when Principal and Amount are givenFormual 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 = $3294 – $3050 = $244
Thus, Simple Interest = $244
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 × 244/3050 × 2
= 24400/6100
= 4 years (using formula)
Thus, Time (T) = 4 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 = $244 (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 $244, then the time = 1/61 × 244 years
= 1 × 244/61 years
= 244/61 = 4 years
Thus, time (T) = 4 years Answer
Similar Questions
(1) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.
(2) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 10% simple interest?
(3) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7392 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.
(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 8 years.
(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 4 years.
(7) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 5% simple interest?
(8) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 2% simple interest?
(9) If Barbara paid $3976 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 4 years.