Question:
In how much time a principal of $3200 will amount to $3456 at a simple interest of 2% per annum?
Correct Answer
4
Solution And Explanation
Solution
Given,
Principal (P) = $3200
Rate of Simple Interest (R) = 2% per annum
Amount (A) = $3456
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 = $3456 – $3200 = $256
Thus, Simple Interest = $256
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 × 256/3200 × 2
= 25600/6400
= 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) = $3200
Rate of Simple Interest (R) = 2% per annum
Simple Interest = $256 (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 $3200
= 2/100 × 3200
= 2 × 3200/100
= 6400/100 = 64
Thus, simple Interest for 1 year = $64
Now,
∵ If the simple Interest is $64, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/64 years
∴ If the simple Interest is $256, then the time = 1/64 × 256 years
= 1 × 256/64 years
= 256/64 = 4 years
Thus, time (T) = 4 years Answer
Similar Questions
(1) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.
(2) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 7 years.
(3) What amount does John have to pay after 5 years if he takes a loan of $3200 at 3% simple interest?
(4) If Jennifer paid $3770 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 2% simple interest?
(6) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 2% simple interest.
(7) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 3 years.
(8) How much loan did Donald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7800 to clear it?
(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 7 years.
(10) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 3 years.