Question:
Donald took a loan of $7000 at the rate of 9% 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
10
Solution And Explanation
Solution
Given,
Principal (P) = $7000
Rate of Simple Interest (R) = 9% 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 × 9
= 630000/63000
= 10 years (using formula)
Thus, Time (T) = 10 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) = 9% 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 = 9% of Principal
= 9% of $7000
= 9/100 × 7000
= 9 × 7000/100
= 63000/100 = 630
Thus, simple Interest for 1 year = $630
Now,
∵ If the simple Interest is $630, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/630 years
∴ If the simple Interest is $6300, then the time = 1/630 × 6300 years
= 1 × 6300/630 years
= 6300/630 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 7 years.
(3) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 10% simple interest?
(4) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 7% simple interest?
(5) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 7% simple interest?
(6) Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 3 years.
(7) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 6% simple interest?
(8) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.
(9) If Mark paid $4752 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 6% simple interest?