Question:
Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12040 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) = 8% per annum
Amount (A) = $12040
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 = $12040 – $7000 = $5040
Thus, Simple Interest = $5040
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 × 5040/7000 × 8
= 504000/56000
= 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) = 8% per annum
Simple Interest = $5040 (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 $5040, then the time = 1/560 × 5040 years
= 1 × 5040/560 years
= 5040/560 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 4% simple interest?
(2) If Michael paid $3828 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(3) Kenneth had to pay $5450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.
(5) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.
(6) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 3% simple interest?
(7) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 2% simple interest?
(8) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 4 years.
(9) William had to pay $3710 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.