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) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8580 to clear it?
(2) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.
(3) In how much time a principal of $3150 will amount to $3433.5 at a simple interest of 3% per annum?
(4) Lisa had to pay $4657.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) Linda had to pay $3752 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 7 years.
(7) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 3% simple interest.
(9) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.
(10) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.