Question:
Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9116 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $9116
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 = $9116 – $5300 = $3816
Thus, Simple Interest = $3816
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 × 3816/5300 × 8
= 381600/42400
= 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) = $5300
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $3816 (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 $5300
= 8/100 × 5300
= 8 × 5300/100
= 42400/100 = 424
Thus, simple Interest for 1 year = $424
Now,
∵ If the simple Interest is $424, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/424 years
∴ If the simple Interest is $3816, then the time = 1/424 × 3816 years
= 1 × 3816/424 years
= 3816/424 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8050 to clear it?
(2) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 3 years.
(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) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 8 years.
(6) Calculate the amount due if Susan borrowed a sum of $3650 at 6% simple interest for 4 years.
(7) What amount will be due after 2 years if David borrowed a sum of $3200 at a 6% simple interest?
(8) Find the amount to be paid if Patricia borrowed a sum of $5150 at 2% simple interest for 7 years.
(9) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 7 years.
(10) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8337.5 to clear it?