Question:
( 1 of 10 ) In how much time a principal of $3200 will amount to $3584 at a simple interest of 3% per annum?
(A) 4 47/50 Or, 247/50
(B) 8 47/50 Or, 447/50
(C) 4 141/50 Or, 341/50
(D) 4 94/50 Or, 294/50
You selected
6
Correct Answer
4
Solution And Explanation
Solution
Given,
Principal (P) = $3200
Rate of Simple Interest (R) = 3% 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 × 3
= 38400/9600
= 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) = 3% 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 = 3% of Principal
= 3% of $3200
= 3/100 × 3200
= 3 × 3200/100
= 9600/100 = 96
Thus, simple Interest for 1 year = $96
Now,
∵ If the simple Interest is $96, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/96 years
∴ If the simple Interest is $384, then the time = 1/96 × 384 years
= 1 × 384/96 years
= 384/96 = 4 years
Thus, time (T) = 4 years Answer
Similar Questions
(1) If William paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 8 years.
(3) Michael had to pay $3498 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 6% simple interest.
(5) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 7 years.
(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 7 years.
(7) What amount does David have to pay after 6 years if he takes a loan of $3400 at 9% simple interest?
(8) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 8% simple interest?
(9) Calculate the amount due if Susan borrowed a sum of $3650 at 8% simple interest for 4 years.
(10) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.