Question:
Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $9460
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 = $9460 – $5500 = $3960
Thus, Simple Interest = $3960
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 × 3960/5500 × 8
= 396000/44000
= 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) = $5500
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $3960 (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 $5500
= 8/100 × 5500
= 8 × 5500/100
= 44000/100 = 440
Thus, simple Interest for 1 year = $440
Now,
∵ If the simple Interest is $440, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/440 years
∴ If the simple Interest is $3960, then the time = 1/440 × 3960 years
= 1 × 3960/440 years
= 3960/440 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 10% simple interest.
(2) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.
(3) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.
(4) If Susan borrowed $3650 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(5) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.
(7) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.
(8) If Nancy paid $4980 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 8 years.
(10) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 7% simple interest?