Question:
Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $4100
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $6560
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 = $6560 – $4100 = $2460
Thus, Simple Interest = $2460
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 × 2460/4100 × 10
= 246000/41000
= 6 years (using formula)
Thus, Time (T) = 6 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) = $4100
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $2460 (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 = 10% of Principal
= 10% of $4100
= 10/100 × 4100
= 10 × 4100/100
= 41000/100 = 410
Thus, simple Interest for 1 year = $410
Now,
∵ If the simple Interest is $410, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/410 years
∴ If the simple Interest is $2460, then the time = 1/410 × 2460 years
= 1 × 2460/410 years
= 2460/410 = 6 years
Thus, time (T) = 6 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) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 9% simple interest?
(3) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 6% simple interest?
(4) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 8% simple interest?
(5) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 3 years.
(6) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Charles borrowed a sum of $3900 at 3% simple interest for 4 years.
(8) Richard had to pay $3816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 7 years.
(10) In how much time a principal of $3150 will amount to $3276 at a simple interest of 2% per annum?