Question:
In how much time a principal of $3150 will amount to $3433.5 at a simple interest of 3% per annum?
Correct Answer
3
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (R) = 3% per annum
Amount (A) = $3433.5
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 = $3433.5 – $3150 = $283.5
Thus, Simple Interest = $283.5
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 × 283.5/3150 × 3
= 28350/9450
= 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) = $3150
Rate of Simple Interest (R) = 3% per annum
Simple Interest = $283.5 (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 $3150
= 3/100 × 3150
= 3 × 3150/100
= 9450/100 = 94.5
Thus, simple Interest for 1 year = $94.5
Now,
∵ If the simple Interest is $94.5, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/94.5 years
∴ If the simple Interest is $283.5, then the time = 1/94.5 × 283.5 years
= 1 × 283.5/94.5 years
= 283.5/94.5 = 3 years
Thus, time (T) = 3 years Answer
Similar Questions
(1) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 7 years.
(2) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.
(3) If James paid $3600 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(4) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $8932 to clear the loan, then find the time period of the loan.
(5) In how much time a principal of $3150 will amount to $3402 at a simple interest of 4% per annum?
(6) How much loan did Anthony borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6930 to clear it?
(7) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 7% simple interest.
(8) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.
(9) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11222 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 10% simple interest.