Question:
In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 5% per annum?
Correct Answer
3
Solution And Explanation
Solution
Given,
Principal (P) = $3050
Rate of Simple Interest (R) = 5% per annum
Amount (A) = $3507.5
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 = $3507.5 – $3050 = $457.5
Thus, Simple Interest = $457.5
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 × 457.5/3050 × 5
= 45750/15250
= 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) = $3050
Rate of Simple Interest (R) = 5% per annum
Simple Interest = $457.5 (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 = 5% of Principal
= 5% of $3050
= 5/100 × 3050
= 5 × 3050/100
= 15250/100 = 152.5
Thus, simple Interest for 1 year = $152.5
Now,
∵ If the simple Interest is $152.5, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/152.5 years
∴ If the simple Interest is $457.5, then the time = 1/152.5 × 457.5 years
= 1 × 457.5/152.5 years
= 457.5/152.5 = 3 years
Thus, time (T) = 3 years Answer
Similar Questions
(1) In how much time a principal of $3200 will amount to $3840 at a simple interest of 4% per annum?
(2) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 10% simple interest?
(3) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 8 years.
(5) Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 7 years.
(6) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 3 years.
(7) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.
(8) If Matthew paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 4% simple interest?
(10) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.