Question:
Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8140 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $8140
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 = $8140 – $5500 = $2640
Thus, Simple Interest = $2640
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 × 2640/5500 × 6
= 264000/33000
= 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) = $5500
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2640 (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 $2640, then the time = 1/330 × 2640 years
= 1 × 2640/330 years
= 2640/330 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 8% simple interest.
(2) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 6% simple interest?
(3) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 5% simple interest?
(4) What amount does James have to pay after 5 years if he takes a loan of $3000 at 9% simple interest?
(5) How much loan did Sarah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7312.5 to clear it?
(6) 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.
(7) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 3 years.
(9) How much loan did Steven borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7920 to clear it?
(10) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 4% simple interest.