Question:
Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $8800
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 = $8800 – $5500 = $3300
Thus, Simple Interest = $3300
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 × 3300/5500 × 6
= 330000/33000
= 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) = $5500
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $3300 (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 = 6% of Principal
= 6% of $5500
= 6/100 × 5500
= 6 × 5500/100
= 33000/100 = 330
Thus, simple Interest for 1 year = $330
Now,
∵ If the simple Interest is $330, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/330 years
∴ If the simple Interest is $3300, then the time = 1/330 × 3300 years
= 1 × 3300/330 years
= 3300/330 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Find the amount to be paid if Susan borrowed a sum of $5650 at 2% simple interest for 7 years.
(2) Calculate the amount due if John borrowed a sum of $3200 at 3% simple interest for 4 years.
(3) How much loan did Sandra borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8062.5 to clear it?
(4) Linda had to pay $3651.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) If Betty paid $5100 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $8736 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Mary borrowed a sum of $5050 at 4% simple interest for 7 years.
(8) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Jennifer borrowed a sum of $3250 at 4% simple interest for 4 years.
(10) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 8 years.