Question:
Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8965 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $8965
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 = $8965 – $5500 = $3465
Thus, Simple Interest = $3465
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 × 3465/5500 × 9
= 346500/49500
= 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) = $5500
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $3465 (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 = 9% of Principal
= 9% of $5500
= 9/100 × 5500
= 9 × 5500/100
= 49500/100 = 495
Thus, simple Interest for 1 year = $495
Now,
∵ If the simple Interest is $495, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/495 years
∴ If the simple Interest is $3465, then the time = 1/495 × 3465 years
= 1 × 3465/495 years
= 3465/495 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Michael had to pay $3597 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(2) In how much time a principal of $3150 will amount to $3528 at a simple interest of 4% per annum?
(3) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.
(4) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.
(5) Elizabeth had to pay $3864 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 4% simple interest?
(7) How much loan did Timothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8880 to clear it?
(8) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 9% simple interest?
(9) How much loan did William borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6325 to clear it?
(10) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.