Question:
Jessica took a loan of $5500 at the rate of 6% 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
9
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (R) = 6% 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 × 6
= 297000/33000
= 9 years (using formula)
Thus, Time (T) = 9 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 = $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 = 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 $2970, then the time = 1/330 × 2970 years
= 1 × 2970/330 years
= 2970/330 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) In how much time a principal of $3200 will amount to $3680 at a simple interest of 3% per annum?
(2) What amount does James have to pay after 6 years if he takes a loan of $3000 at 10% simple interest?
(3) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.
(4) How much loan did Barbara borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6937.5 to clear it?
(5) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 8 years.
(6) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 10% simple interest?
(7) 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.
(8) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.
(9) What amount does William have to pay after 5 years if he takes a loan of $3500 at 10% simple interest?
(10) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.