Question:
In how much time a principal of $3050 will amount to $3324.5 at a simple interest of 3% per annum?
Correct Answer
3
Solution And Explanation
Solution
Given,
Principal (P) = $3050
Rate of Simple Interest (R) = 3% per annum
Amount (A) = $3324.5
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 = $3324.5 – $3050 = $274.5
Thus, Simple Interest = $274.5
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 × 274.5/3050 × 3
= 27450/9150
= 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) = $3050
Rate of Simple Interest (R) = 3% per annum
Simple Interest = $274.5 (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 = 3% of Principal
= 3% of $3050
= 3/100 × 3050
= 3 × 3050/100
= 9150/100 = 91.5
Thus, simple Interest for 1 year = $91.5
Now,
∵ If the simple Interest is $91.5, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/91.5 years
∴ If the simple Interest is $274.5, then the time = 1/91.5 × 274.5 years
= 1 × 274.5/91.5 years
= 274.5/91.5 = 3 years
Thus, time (T) = 3 years Answer
Similar Questions
(1) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 9% simple interest?
(2) If Margaret paid $5046 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(3) If Jennifer borrowed $3250 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(4) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 7% simple interest for 7 years.
(6) Patricia had to pay $3528 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 2% simple interest?
(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 3 years.
(9) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 7 years.
(10) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?