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) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 3 years.
(2) Calculate the amount due if Joseph borrowed a sum of $3700 at 5% simple interest for 4 years.
(3) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.
(4) How much loan did Mary borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6312.5 to clear it?
(5) If James borrowed $3000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(6) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 6% simple interest?
(7) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.
(8) If Joshua paid $5292 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) What amount does James have to pay after 5 years if he takes a loan of $3000 at 2% simple interest?
(10) How much loan did Anthony borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7245 to clear it?