Question:
Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $10920 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $7000
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $10920
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 = $10920 – $7000 = $3920
Thus, Simple Interest = $3920
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 × 3920/7000 × 8
= 392000/56000
= 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) = $7000
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $3920 (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 $7000
= 8/100 × 7000
= 8 × 7000/100
= 56000/100 = 560
Thus, simple Interest for 1 year = $560
Now,
∵ If the simple Interest is $560, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/560 years
∴ If the simple Interest is $3920, then the time = 1/560 × 3920 years
= 1 × 3920/560 years
= 3920/560 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Calculate the amount due if Barbara borrowed a sum of $3550 at 8% simple interest for 3 years.
(2) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.
(3) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 5% simple interest?
(4) Calculate the amount due if Patricia borrowed a sum of $3150 at 2% simple interest for 3 years.
(5) How much loan did Michelle borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7992.5 to clear it?
(6) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.
(7) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 6% simple interest?
(8) Find the amount to be paid if John borrowed a sum of $5200 at 6% simple interest for 7 years.
(9) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $7952 to clear the loan, then find the time period of the loan.
(10) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $7888 to clear the loan, then find the time period of the loan.