Question:
Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10281 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $6900
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $10281
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 = $10281 – $6900 = $3381
Thus, Simple Interest = $3381
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 × 3381/6900 × 7
= 338100/48300
= 7 years (using formula)
Thus, Time (T) = 7 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) = $6900
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $3381 (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 $6900
= 7/100 × 6900
= 7 × 6900/100
= 48300/100 = 483
Thus, simple Interest for 1 year = $483
Now,
∵ If the simple Interest is $483, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/483 years
∴ If the simple Interest is $3381, then the time = 1/483 × 3381 years
= 1 × 3381/483 years
= 3381/483 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) How much loan did Jessica borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6325 to clear it?
(2) How much loan did Jacob borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9600 to clear it?
(3) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.
(4) Susan had to pay $3978.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 8% simple interest?
(6) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 10% simple interest?
(7) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 3% simple interest?
(8) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 8 years.
(9) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 7 years.