Question:
John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7216 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4400
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $7216
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 = $7216 – $4400 = $2816
Thus, Simple Interest = $2816
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 × 2816/4400 × 8
= 281600/35200
= 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) = $4400
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $2816 (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 $4400
= 8/100 × 4400
= 8 × 4400/100
= 35200/100 = 352
Thus, simple Interest for 1 year = $352
Now,
∵ If the simple Interest is $352, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/352 years
∴ If the simple Interest is $2816, then the time = 1/352 × 2816 years
= 1 × 2816/352 years
= 2816/352 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 7% simple interest?
(2) Susan had to pay $4088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 3% simple interest.
(4) How much loan did Ronald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8250 to clear it?
(5) How much loan did Jessica borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6612.5 to clear it?
(6) Calculate the amount due if James borrowed a sum of $3000 at 3% simple interest for 4 years.
(7) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $9828 to clear the loan, then find the time period of the loan.
(8) In how much time a principal of $3000 will amount to $3450 at a simple interest of 5% per annum?
(9) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 2% simple interest?
(10) Calculate the amount due if Charles borrowed a sum of $3900 at 9% simple interest for 4 years.