Question:
Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $9676 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $9676
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 = $9676 – $5900 = $3776
Thus, Simple Interest = $3776
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 × 3776/5900 × 8
= 377600/47200
= 8 years (using formula)
Thus, Time (T) = 8 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) = $5900
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $3776 (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 $5900
= 8/100 × 5900
= 8 × 5900/100
= 47200/100 = 472
Thus, simple Interest for 1 year = $472
Now,
∵ If the simple Interest is $472, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/472 years
∴ If the simple Interest is $3776, then the time = 1/472 × 3776 years
= 1 × 3776/472 years
= 3776/472 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) If Joseph borrowed $3700 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(2) Find the amount to be paid if David borrowed a sum of $5400 at 6% simple interest for 7 years.
(3) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan.
(4) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11247 to clear the loan, then find the time period of the loan.
(5) What amount does James have to pay after 5 years if he takes a loan of $3000 at 7% simple interest?
(6) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 8% simple interest?
(7) Mary had to pay $3233 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) What amount does John have to pay after 5 years if he takes a loan of $3200 at 5% simple interest?
(9) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 7 years.
(10) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.