Question:
Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $4500
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $6930
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 = $6930 – $4500 = $2430
Thus, Simple Interest = $2430
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 × 2430/4500 × 9
= 243000/40500
= 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) = $4500
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $2430 (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 $4500
= 9/100 × 4500
= 9 × 4500/100
= 40500/100 = 405
Thus, simple Interest for 1 year = $405
Now,
∵ If the simple Interest is $405, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/405 years
∴ If the simple Interest is $2430, then the time = 1/405 × 2430 years
= 1 × 2430/405 years
= 2430/405 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Emily had to pay $5035 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8856 to clear the loan, then find the time period of the loan.
(3) How much loan did Steven borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7920 to clear it?
(4) Calculate the amount due if Karen borrowed a sum of $3950 at 7% simple interest for 3 years.
(5) In how much time a principal of $3200 will amount to $3488 at a simple interest of 3% per annum?
(6) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 7% simple interest?
(7) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.
(8) What amount does James have to pay after 6 years if he takes a loan of $3000 at 4% simple interest?
(9) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9310 to clear the loan, then find the time period of the loan.
(10) How much loan did Ryan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9480 to clear it?