Question:
Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9685 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) = 7% per annum
Amount (A) = $9685
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 = $9685 – $6500 = $3185
Thus, Simple Interest = $3185
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 × 3185/6500 × 7
= 318500/45500
= 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) = 7% per annum
Simple Interest = $3185 (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 $6500
= 7/100 × 6500
= 7 × 6500/100
= 45500/100 = 455
Thus, simple Interest for 1 year = $455
Now,
∵ If the simple Interest is $455, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/455 years
∴ If the simple Interest is $3185, then the time = 1/455 × 3185 years
= 1 × 3185/455 years
= 3185/455 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9116 to clear the loan, then find the time period of the loan.
(2) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 9% simple interest?
(3) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 8 years.
(4) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 5% simple interest?
(5) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $8100 to clear the loan, then find the time period of the loan.
(6) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 2% simple interest?
(7) How much loan did Steven borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8250 to clear it?
(8) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7980 to clear it?
(9) Barbara took a loan of $5100 at the rate of 10% 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 if Sarah borrowed a sum of $3850 at 2% simple interest for 4 years.