Question:
In how much time a principal of $3050 will amount to $3355 at a simple interest of 2% per annum?
Correct Answer
5
Solution And Explanation
Solution
Given,
Principal (P) = $3050
Rate of Simple Interest (R) = 2% 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 × 2
= 30500/6100
= 5 years (using formula)
Thus, Time (T) = 5 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 = $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 = 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 $305, then the time = 1/61 × 305 years
= 1 × 305/61 years
= 305/61 = 5 years
Thus, time (T) = 5 years Answer
Similar Questions
(1) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.
(2) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 7% simple interest?
(3) What amount does James have to pay after 6 years if he takes a loan of $3000 at 5% simple interest?
(4) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 5% simple interest?
(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 4 years.
(6) In how much time a principal of $3200 will amount to $3840 at a simple interest of 5% per annum?
(7) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
(8) What amount does William have to pay after 6 years if he takes a loan of $3500 at 7% simple interest?
(9) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 10% simple interest?
(10) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 7 years.