Question:
Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8820 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4900
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $8820
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 = $8820 – $4900 = $3920
Thus, Simple Interest = $3920
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 × 3920/4900 × 10
= 392000/49000
= 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) = $4900
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $3920 (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 = 10% of Principal
= 10% of $4900
= 10/100 × 4900
= 10 × 4900/100
= 49000/100 = 490
Thus, simple Interest for 1 year = $490
Now,
∵ If the simple Interest is $490, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/490 years
∴ If the simple Interest is $3920, then the time = 1/490 × 3920 years
= 1 × 3920/490 years
= 3920/490 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 3% simple interest?
(2) In how much time a principal of $3000 will amount to $3270 at a simple interest of 3% per annum?
(3) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.
(4) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7488 to clear the loan, then find the time period of the loan.
(5) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $6468 to clear the loan, then find the time period of the loan.
(6) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 4% simple interest?
(8) How much loan did Emily borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8100 to clear it?
(9) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 4% simple interest?
(10) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.