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) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 5% simple interest?
(2) How much loan did Richard borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6440 to clear it?
(3) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 3 years.
(4) What amount does William have to pay after 6 years if he takes a loan of $3500 at 10% simple interest?
(5) In how much time a principal of $3150 will amount to $3276 at a simple interest of 2% per annum?
(6) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.
(7) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.
(8) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8145 to clear the loan, then find the time period of the loan.
(9) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9062.5 to clear it?
(10) If Christopher borrowed $4000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.