Question:
Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9672 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $6200
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $9672
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 = $9672 – $6200 = $3472
Thus, Simple Interest = $3472
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 × 3472/6200 × 8
= 347200/49600
= 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) = $6200
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $3472 (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 = 8% of Principal
= 8% of $6200
= 8/100 × 6200
= 8 × 6200/100
= 49600/100 = 496
Thus, simple Interest for 1 year = $496
Now,
∵ If the simple Interest is $496, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/496 years
∴ If the simple Interest is $3472, then the time = 1/496 × 3472 years
= 1 × 3472/496 years
= 3472/496 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 3% simple interest?
(2) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 6% simple interest?
(3) Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 3 years.
(4) Find the amount to be paid if Patricia borrowed a sum of $5150 at 2% simple interest for 8 years.
(5) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7498 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Charles borrowed a sum of $3900 at 2% simple interest for 3 years.
(7) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 4% simple interest.
(8) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 4% simple interest.
(9) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 4% simple interest.
(10) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.