Question:
Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $7000
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $13300
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 = $13300 – $7000 = $6300
Thus, Simple Interest = $6300
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 × 6300/7000 × 10
= 630000/70000
= 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) = $7000
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $6300 (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 = 10% of Principal
= 10% of $7000
= 10/100 × 7000
= 10 × 7000/100
= 70000/100 = 700
Thus, simple Interest for 1 year = $700
Now,
∵ If the simple Interest is $700, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/700 years
∴ If the simple Interest is $6300, then the time = 1/700 × 6300 years
= 1 × 6300/700 years
= 6300/700 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Find the amount to be paid if David borrowed a sum of $5400 at 3% simple interest for 8 years.
(2) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 2% simple interest.
(3) Find the amount to be paid if Thomas borrowed a sum of $5800 at 3% simple interest for 7 years.
(4) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $11900 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 7 years.
(6) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 8 years.
(8) What amount does John have to pay after 5 years if he takes a loan of $3200 at 2% simple interest?
(9) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8745 to clear it?
(10) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.