Question:
In how much time a principal of $3050 will amount to $3233 at a simple interest of 3% per annum?
Correct Answer
2
Solution And Explanation
Solution
Given,
Principal (P) = $3050
Rate of Simple Interest (R) = 3% per annum
Amount (A) = $3233
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 = $3233 – $3050 = $183
Thus, Simple Interest = $183
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 × 183/3050 × 3
= 18300/9150
= 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) = 3% per annum
Simple Interest = $183 (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 $183, then the time = 1/91.5 × 183 years
= 1 × 183/91.5 years
= 183/91.5 = 2 years
Thus, time (T) = 2 years Answer
Similar Questions
(1) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10988 to clear the loan, then find the time period of the loan.
(2) In how much time a principal of $3000 will amount to $3360 at a simple interest of 4% per annum?
(3) How much loan did Sarah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7312.5 to clear it?
(4) Find the amount to be paid if Michael borrowed a sum of $5300 at 8% simple interest for 7 years.
(5) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 8% simple interest.
(6) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 10% simple interest?
(7) If Charles borrowed $3900 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(8) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.
(9) Charles had to pay $4134 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 7% simple interest.