Question:
In how much time a principal of $3050 will amount to $3355 at a simple interest of 5% per annum?
Correct Answer
2
Solution And Explanation
Solution
Given,
Principal (P) = $3050
Rate of Simple Interest (R) = 5% per annum
Amount (A) = $3355
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 = $3355 – $3050 = $305
Thus, Simple Interest = $305
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 × 305/3050 × 5
= 30500/15250
= 2 years (using formula)
Thus, Time (T) = 2 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) = 5% per annum
Simple Interest = $305 (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 $3050
= 5/100 × 3050
= 5 × 3050/100
= 15250/100 = 152.5
Thus, simple Interest for 1 year = $152.5
Now,
∵ If the simple Interest is $152.5, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/152.5 years
∴ If the simple Interest is $305, then the time = 1/152.5 × 305 years
= 1 × 305/152.5 years
= 305/152.5 = 2 years
Thus, time (T) = 2 years Answer
Similar Questions
(1) Kimberly had to pay $5347.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) Find the amount to be paid if Robert borrowed a sum of $5100 at 6% simple interest for 7 years.
(3) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 9% simple interest?
(4) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 8% simple interest?
(5) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 7% simple interest?
(6) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.
(7) In how much time a principal of $3150 will amount to $3937.5 at a simple interest of 5% per annum?
(8) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.
(9) Calculate the amount due if Charles borrowed a sum of $3900 at 6% simple interest for 4 years.
(10) Find the amount to be paid if Richard borrowed a sum of $5600 at 4% simple interest for 8 years.