Question:
David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4800
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $8256
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 = $8256 – $4800 = $3456
Thus, Simple Interest = $3456
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 × 3456/4800 × 9
= 345600/43200
= 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) = $4800
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $3456 (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 $4800
= 9/100 × 4800
= 9 × 4800/100
= 43200/100 = 432
Thus, simple Interest for 1 year = $432
Now,
∵ If the simple Interest is $432, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/432 years
∴ If the simple Interest is $3456, then the time = 1/432 × 3456 years
= 1 × 3456/432 years
= 3456/432 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.
(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 7 years.
(3) In how much time a principal of $3200 will amount to $3840 at a simple interest of 5% per annum?
(4) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $6936 to clear the loan, then find the time period of the loan.
(5) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 8 years.
(7) If Susan paid $4234 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 4% simple interest?
(9) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 10% simple interest?
(10) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.