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) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.
(2) If Charles paid $4680 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) Daniel had to pay $4592 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(4) Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 8 years.
(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 4 years.
(6) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 7% simple interest?
(7) Calculate the amount due if Charles borrowed a sum of $3900 at 2% simple interest for 4 years.
(8) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 5% simple interest?
(9) How much loan did Mary borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5807.5 to clear it?
(10) Calculate the amount due if Linda borrowed a sum of $3350 at 6% simple interest for 3 years.