Question:
Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4700
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $7332
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 = $7332 – $4700 = $2632
Thus, Simple Interest = $2632
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 × 2632/4700 × 7
= 263200/32900
= 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) = $4700
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $2632 (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 = 7% of Principal
= 7% of $4700
= 7/100 × 4700
= 7 × 4700/100
= 32900/100 = 329
Thus, simple Interest for 1 year = $329
Now,
∵ If the simple Interest is $329, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/329 years
∴ If the simple Interest is $2632, then the time = 1/329 × 2632 years
= 1 × 2632/329 years
= 2632/329 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) In how much time a principal of $3100 will amount to $3472 at a simple interest of 3% per annum?
(2) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 6% simple interest?
(3) Steven had to pay $4876 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 7 years.
(5) If Daniel paid $4592 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
(7) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8337.5 to clear it?
(8) Anthony had to pay $4558 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.