Question:
In how much time a principal of $3150 will amount to $3402 at a simple interest of 2% per annum?
Correct Answer
4
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (R) = 2% per annum
Amount (A) = $3402
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 = $3402 – $3150 = $252
Thus, Simple Interest = $252
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 × 252/3150 × 2
= 25200/6300
= 4 years (using formula)
Thus, Time (T) = 4 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) = 2% per annum
Simple Interest = $252 (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 = 2% of Principal
= 2% of $3150
= 2/100 × 3150
= 2 × 3150/100
= 6300/100 = 63
Thus, simple Interest for 1 year = $63
Now,
∵ If the simple Interest is $63, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/63 years
∴ If the simple Interest is $252, then the time = 1/63 × 252 years
= 1 × 252/63 years
= 252/63 = 4 years
Thus, time (T) = 4 years Answer
Similar Questions
(1) Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 7 years.
(2) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.
(3) Find the amount to be paid if Susan borrowed a sum of $5650 at 5% simple interest for 8 years.
(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 7 years.
(5) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 6% simple interest?
(6) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 4 years.
(7) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 7 years.
(8) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7602 to clear the loan, then find the time period of the loan.
(9) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 6% simple interest?
(10) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 4 years.