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) In how much time a principal of $3000 will amount to $3180 at a simple interest of 2% per annum?
(2) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 8 years.
(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 8 years.
(4) How much loan did Sharon borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9687.5 to clear it?
(5) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7526 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 6% simple interest?
(7) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 4 years.
(8) Find the amount to be paid if Karen borrowed a sum of $5950 at 6% simple interest for 7 years.
(9) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 2% simple interest?
(10) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 4% simple interest?