Question:
Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $4900
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $7546
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 = $7546 – $4900 = $2646
Thus, Simple Interest = $2646
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 × 2646/4900 × 9
= 264600/44100
= 6 years (using formula)
Thus, Time (T) = 6 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) = $4900
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $2646 (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 $4900
= 9/100 × 4900
= 9 × 4900/100
= 44100/100 = 441
Thus, simple Interest for 1 year = $441
Now,
∵ If the simple Interest is $441, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/441 years
∴ If the simple Interest is $2646, then the time = 1/441 × 2646 years
= 1 × 2646/441 years
= 2646/441 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Find the amount to be paid if Richard borrowed a sum of $5600 at 2% simple interest for 8 years.
(2) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 2% simple interest?
(3) In how much time a principal of $3200 will amount to $3584 at a simple interest of 3% per annum?
(4) If Joseph borrowed $3700 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(5) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 4% simple interest?
(6) How much loan did Sarah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6727.5 to clear it?
(7) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 4% simple interest?
(8) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5920 to clear the loan, then find the time period of the loan.
(9) How much loan did Joseph borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6555 to clear it?
(10) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 3% simple interest?