Question:
Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $8670
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 = $8670 – $5100 = $3570
Thus, Simple Interest = $3570
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 × 3570/5100 × 7
= 357000/35700
= 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) = $5100
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $3570 (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 $5100
= 7/100 × 5100
= 7 × 5100/100
= 35700/100 = 357
Thus, simple Interest for 1 year = $357
Now,
∵ If the simple Interest is $357, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/357 years
∴ If the simple Interest is $3570, then the time = 1/357 × 3570 years
= 1 × 3570/357 years
= 3570/357 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8288 to clear the loan, then find the time period of the loan.
(2) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 4% simple interest.
(4) What amount will be due after 2 years if James borrowed a sum of $3000 at a 6% simple interest?
(5) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.
(6) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.
(8) In how much time a principal of $3050 will amount to $3233 at a simple interest of 3% per annum?
(9) In how much time a principal of $3200 will amount to $3520 at a simple interest of 2% per annum?
(10) David had to pay $3910 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.