Question:
In how much time a principal of $3150 will amount to $3528 at a simple interest of 3% per annum?
Correct Answer
4
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (R) = 3% per annum
Amount (A) = $3528
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 = $3528 – $3150 = $378
Thus, Simple Interest = $378
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 × 378/3150 × 3
= 37800/9450
= 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) = $3150
Rate of Simple Interest (R) = 3% per annum
Simple Interest = $378 (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 $3150
= 3/100 × 3150
= 3 × 3150/100
= 9450/100 = 94.5
Thus, simple Interest for 1 year = $94.5
Now,
∵ If the simple Interest is $94.5, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/94.5 years
∴ If the simple Interest is $378, then the time = 1/94.5 × 378 years
= 1 × 378/94.5 years
= 378/94.5 = 4 years
Thus, time (T) = 4 years Answer
Similar Questions
(1) Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 8 years.
(2) Calculate the amount due if Thomas borrowed a sum of $3800 at 4% simple interest for 3 years.
(3) How much loan did Sarah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6435 to clear it?
(4) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 2% simple interest?
(5) John had to pay $3488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) What amount does David have to pay after 6 years if he takes a loan of $3400 at 8% simple interest?
(7) If Mary paid $3416 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(8) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 6% simple interest?
(9) Calculate the amount due if Mary borrowed a sum of $3050 at 5% simple interest for 3 years.
(10) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.