Question:
Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $4900
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $7644
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 = $7644 – $4900 = $2744
Thus, Simple Interest = $2744
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 × 2744/4900 × 8
= 274400/39200
= 7 years (using formula)
Thus, Time (T) = 7 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) = $4900
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $2744 (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 = 8% of Principal
= 8% of $4900
= 8/100 × 4900
= 8 × 4900/100
= 39200/100 = 392
Thus, simple Interest for 1 year = $392
Now,
∵ If the simple Interest is $392, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/392 years
∴ If the simple Interest is $2744, then the time = 1/392 × 2744 years
= 1 × 2744/392 years
= 2744/392 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Calculate the amount due if Thomas borrowed a sum of $3800 at 10% simple interest for 4 years.
(2) How much loan did Ryan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9875 to clear it?
(3) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 6% simple interest?
(4) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 10% simple interest?
(5) How much loan did Ashley borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7205 to clear it?
(6) In how much time a principal of $3000 will amount to $3180 at a simple interest of 2% per annum?
(7) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 4% simple interest?
(8) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 8% simple interest?
(9) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 8% simple interest.
(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 3 years.