Question:
Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $8100 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4500
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $8100
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 = $8100 – $4500 = $3600
Thus, Simple Interest = $3600
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 × 3600/4500 × 10
= 360000/45000
= 8 years (using formula)
Thus, Time (T) = 8 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) = $4500
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $3600 (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 = 10% of Principal
= 10% of $4500
= 10/100 × 4500
= 10 × 4500/100
= 45000/100 = 450
Thus, simple Interest for 1 year = $450
Now,
∵ If the simple Interest is $450, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/450 years
∴ If the simple Interest is $3600, then the time = 1/450 × 3600 years
= 1 × 3600/450 years
= 3600/450 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 8 years.
(2) If Joseph borrowed $3700 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(3) Find the amount to be paid if Joseph borrowed a sum of $5700 at 6% simple interest for 8 years.
(4) What amount will be due after 2 years if John borrowed a sum of $3100 at a 7% simple interest?
(5) How much loan did Patricia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5665 to clear it?
(6) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 6% simple interest.
(7) Robert had to pay $3565 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 3% simple interest?
(9) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 3% simple interest?
(10) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10168 to clear the loan, then find the time period of the loan.