Question:
Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8930 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $4700
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $8930
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 = $8930 – $4700 = $4230
Thus, Simple Interest = $4230
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 × 4230/4700 × 9
= 423000/42300
= 10 years (using formula)
Thus, Time (T) = 10 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) = $4700
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $4230 (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 $4700
= 9/100 × 4700
= 9 × 4700/100
= 42300/100 = 423
Thus, simple Interest for 1 year = $423
Now,
∵ If the simple Interest is $423, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/423 years
∴ If the simple Interest is $4230, then the time = 1/423 × 4230 years
= 1 × 4230/423 years
= 4230/423 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Margaret had to pay $5002.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) In how much time a principal of $3150 will amount to $3465 at a simple interest of 2% per annum?
(3) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7240 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 8 years.
(5) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 5% simple interest.
(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 7 years.
(7) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 6% simple interest?
(8) How much loan did Timothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8140 to clear it?
(9) Find the amount to be paid if James borrowed a sum of $5000 at 4% simple interest for 8 years.
(10) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 3% simple interest?