Question:
Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $6500
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $9230
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 = $9230 – $6500 = $2730
Thus, Simple Interest = $2730
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 × 2730/6500 × 6
= 273000/39000
= 7 years (using formula)
Thus, Time (T) = 7 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) = $6500
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2730 (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 = 6% of Principal
= 6% of $6500
= 6/100 × 6500
= 6 × 6500/100
= 39000/100 = 390
Thus, simple Interest for 1 year = $390
Now,
∵ If the simple Interest is $390, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/390 years
∴ If the simple Interest is $2730, then the time = 1/390 × 2730 years
= 1 × 2730/390 years
= 2730/390 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 4% simple interest.
(2) Daniel had to pay $4592 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) How much loan did Joshua borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7590 to clear it?
(4) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.
(5) In how much time a principal of $3050 will amount to $3233 at a simple interest of 3% per annum?
(6) Margaret had to pay $4741.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $8932 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 7 years.
(9) In how much time a principal of $3000 will amount to $3600 at a simple interest of 4% per annum?
(10) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 8 years.