Question:
In how much time a principal of $3200 will amount to $3584 at a simple interest of 4% per annum?
Correct Answer
3
Solution And Explanation
Solution
Given,
Principal (P) = $3200
Rate of Simple Interest (R) = 4% per annum
Amount (A) = $3584
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 = $3584 – $3200 = $384
Thus, Simple Interest = $384
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 × 384/3200 × 4
= 38400/12800
= 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) = $3200
Rate of Simple Interest (R) = 4% per annum
Simple Interest = $384 (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 $384, then the time = 1/128 × 384 years
= 1 × 384/128 years
= 384/128 = 3 years
Thus, time (T) = 3 years Answer
Similar Questions
(1) How much loan did Timothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8510 to clear it?
(2) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 9% simple interest?
(3) In how much time a principal of $3050 will amount to $3812.5 at a simple interest of 5% per annum?
(4) If Patricia borrowed $3150 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(5) If Mary paid $3660 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6674 to clear the loan, then find the time period of the loan.
(7) How much loan did Donald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7150 to clear it?
(8) How much loan did Sharon borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8912.5 to clear it?
(9) Nancy had to pay $4772.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 8 years.