Question:
Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4600
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $7176
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 = $7176 – $4600 = $2576
Thus, Simple Interest = $2576
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 × 2576/4600 × 7
= 257600/32200
= 8 years (using formula)
Thus, Time (T) = 8 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 = $2576 (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 $2576, then the time = 1/322 × 2576 years
= 1 × 2576/322 years
= 2576/322 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 6% simple interest?
(2) How much loan did Deborah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9312.5 to clear it?
(3) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.
(4) What amount does William have to pay after 6 years if he takes a loan of $3500 at 9% simple interest?
(5) How much loan did Ashley borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7205 to clear it?
(6) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.
(7) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.
(8) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 10% simple interest?
(9) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10106 to clear the loan, then find the time period of the loan.
(10) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.