Question:
Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8470 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $8470
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 = $8470 – $5500 = $2970
Thus, Simple Interest = $2970
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 × 2970/5500 × 9
= 297000/49500
= 6 years (using formula)
Thus, Time (T) = 6 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) = 9% per annum
Simple Interest = $2970 (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 $5500
= 9/100 × 5500
= 9 × 5500/100
= 49500/100 = 495
Thus, simple Interest for 1 year = $495
Now,
∵ If the simple Interest is $495, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/495 years
∴ If the simple Interest is $2970, then the time = 1/495 × 2970 years
= 1 × 2970/495 years
= 2970/495 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 8 years.
(2) How much loan did Thomas borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6380 to clear it?
(3) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 7 years.
(4) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $12489 to clear the loan, then find the time period of the loan.
(5) Anthony had to pay $4945 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 6% simple interest?
(7) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 2% simple interest.
(8) In how much time a principal of $3200 will amount to $3840 at a simple interest of 4% per annum?
(9) If David paid $3808 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) In how much time a principal of $3200 will amount to $3712 at a simple interest of 4% per annum?