Question:
Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9020 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $9020
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 = $9020 – $5500 = $3520
Thus, Simple Interest = $3520
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 × 3520/5500 × 8
= 352000/44000
= 8 years (using formula)
Thus, Time (T) = 8 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 = $3520 (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 $3520, then the time = 1/440 × 3520 years
= 1 × 3520/440 years
= 3520/440 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 8 years.
(2) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 8% simple interest?
(3) In how much time a principal of $3100 will amount to $3410 at a simple interest of 5% per annum?
(4) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.
(5) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 7% simple interest?
(6) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 7% simple interest?
(7) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if John borrowed a sum of $3100 at a 9% simple interest?
(9) Calculate the amount due if Linda borrowed a sum of $3350 at 6% simple interest for 4 years.
(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 3 years.