Question:
In how much time a principal of $3200 will amount to $3456 at a simple interest of 4% per annum?
Correct Answer
2
Solution And Explanation
Solution
Given,
Principal (P) = $3200
Rate of Simple Interest (R) = 4% 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 × 4
= 25600/12800
= 2 years (using formula)
Thus, Time (T) = 2 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) = 4% 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 = 4% of Principal
= 4% of $3200
= 4/100 × 3200
= 4 × 3200/100
= 12800/100 = 128
Thus, simple Interest for 1 year = $128
Now,
∵ If the simple Interest is $128, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/128 years
∴ If the simple Interest is $256, then the time = 1/128 × 256 years
= 1 × 256/128 years
= 256/128 = 2 years
Thus, time (T) = 2 years Answer
Similar Questions
(1) How much loan did Andrew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7480 to clear it?
(2) In how much time a principal of $3200 will amount to $4000 at a simple interest of 5% per annum?
(3) What amount does John have to pay after 6 years if he takes a loan of $3200 at 5% simple interest?
(4) Kimberly had to pay $5208 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11316 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 7 years.
(7) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $12540 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if John borrowed a sum of $5200 at 4% simple interest for 8 years.
(9) How much loan did Michael borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6360 to clear it?
(10) If James paid $3480 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.