Question:
Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $4600
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $7820
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 = $7820 – $4600 = $3220
Thus, Simple Interest = $3220
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 × 3220/4600 × 7
= 322000/32200
= 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) = $4600
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $3220 (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 $4600
= 7/100 × 4600
= 7 × 4600/100
= 32200/100 = 322
Thus, simple Interest for 1 year = $322
Now,
∵ If the simple Interest is $322, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/322 years
∴ If the simple Interest is $3220, then the time = 1/322 × 3220 years
= 1 × 3220/322 years
= 3220/322 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) What amount does William have to pay after 6 years if he takes a loan of $3500 at 5% simple interest?
(2) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 2% simple interest.
(3) In how much time a principal of $3100 will amount to $3565 at a simple interest of 5% per annum?
(4) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.
(5) Christopher had to pay $4480 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.
(7) Calculate the amount due if William borrowed a sum of $3500 at 10% simple interest for 4 years.
(8) How much loan did Donald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8125 to clear it?
(9) Calculate the amount due if Linda borrowed a sum of $3350 at 7% simple interest for 3 years.
(10) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 8 years.