Question:
In how much time a principal of $3000 will amount to $3360 at a simple interest of 4% per annum?
Correct Answer
3
Solution And Explanation
Solution
Given,
Principal (P) = $3000
Rate of Simple Interest (R) = 4% per annum
Amount (A) = $3360
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 = $3360 – $3000 = $360
Thus, Simple Interest = $360
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 × 360/3000 × 4
= 36000/12000
= 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) = $3000
Rate of Simple Interest (R) = 4% per annum
Simple Interest = $360 (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 = 4% of Principal
= 4% of $3000
= 4/100 × 3000
= 4 × 3000/100
= 12000/100 = 120
Thus, simple Interest for 1 year = $120
Now,
∵ If the simple Interest is $120, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/120 years
∴ If the simple Interest is $360, then the time = 1/120 × 360 years
= 1 × 360/120 years
= 360/120 = 3 years
Thus, time (T) = 3 years Answer
Similar Questions
(1) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 6% simple interest?
(2) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9116 to clear the loan, then find the time period of the loan.
(3) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $9291 to clear the loan, then find the time period of the loan.
(4) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 4% simple interest?
(5) In how much time a principal of $3000 will amount to $3180 at a simple interest of 3% per annum?
(6) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7975 to clear it?
(7) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 5% simple interest?
(8) What amount does William have to pay after 5 years if he takes a loan of $3500 at 3% simple interest?
(9) If Anthony paid $5160 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 3 years.