Question:
Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $6900
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $13110
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 = $13110 – $6900 = $6210
Thus, Simple Interest = $6210
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 × 6210/6900 × 9
= 621000/62100
= 10 years (using formula)
Thus, Time (T) = 10 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) = $6900
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $6210 (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 = 9% of Principal
= 9% of $6900
= 9/100 × 6900
= 9 × 6900/100
= 62100/100 = 621
Thus, simple Interest for 1 year = $621
Now,
∵ If the simple Interest is $621, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/621 years
∴ If the simple Interest is $6210, then the time = 1/621 × 6210 years
= 1 × 6210/621 years
= 6210/621 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $8550 to clear the loan, then find the time period of the loan.
(2) In how much time a principal of $3050 will amount to $3233 at a simple interest of 3% per annum?
(3) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Susan borrowed a sum of $5650 at 4% simple interest for 7 years.
(5) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 3 years.
(7) In how much time a principal of $3000 will amount to $3180 at a simple interest of 2% per annum?
(8) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 4% simple interest?
(9) If David paid $3944 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.