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) If James borrowed $3000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 7 years.
(3) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.
(4) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 4% simple interest?
(5) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 8% simple interest?
(6) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.
(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 8 years.
(8) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 3% simple interest?
(9) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 7% simple interest?
(10) Find the amount to be paid if Michael borrowed a sum of $5300 at 7% simple interest for 8 years.