Question:
Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $6200
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $8804
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 = $8804 – $6200 = $2604
Thus, Simple Interest = $2604
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 × 2604/6200 × 7
= 260400/43400
= 6 years (using formula)
Thus, Time (T) = 6 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) = $6200
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $2604 (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 = 7% of Principal
= 7% of $6200
= 7/100 × 6200
= 7 × 6200/100
= 43400/100 = 434
Thus, simple Interest for 1 year = $434
Now,
∵ If the simple Interest is $434, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/434 years
∴ If the simple Interest is $2604, then the time = 1/434 × 2604 years
= 1 × 2604/434 years
= 2604/434 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8930 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 7 years.
(3) In how much time a principal of $3200 will amount to $3584 at a simple interest of 3% per annum?
(4) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 8 years.
(5) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 9% simple interest?
(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 8 years.
(7) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 5% simple interest?
(8) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 4% simple interest.
(9) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 9% simple interest.