Question:
Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $6200
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $9920
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 = $9920 – $6200 = $3720
Thus, Simple Interest = $3720
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 × 3720/6200 × 6
= 372000/37200
= 10 years (using formula)
Thus, Time (T) = 10 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) = 6% per annum
Simple Interest = $3720 (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 $6200
= 6/100 × 6200
= 6 × 6200/100
= 37200/100 = 372
Thus, simple Interest for 1 year = $372
Now,
∵ If the simple Interest is $372, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/372 years
∴ If the simple Interest is $3720, then the time = 1/372 × 3720 years
= 1 × 3720/372 years
= 3720/372 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) How much loan did Jessica borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6325 to clear it?
(2) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 7 years.
(3) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 3% simple interest?
(4) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 7% simple interest?
(5) Mary had to pay $3416 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 7% simple interest?
(7) Andrew had to pay $5232 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.
(9) If Michelle paid $5346 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.