Question:
Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $7000
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $12600
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 = $12600 – $7000 = $5600
Thus, Simple Interest = $5600
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 × 5600/7000 × 8
= 560000/56000
= 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) = $7000
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $5600 (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 $7000
= 8/100 × 7000
= 8 × 7000/100
= 56000/100 = 560
Thus, simple Interest for 1 year = $560
Now,
∵ If the simple Interest is $560, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/560 years
∴ If the simple Interest is $5600, then the time = 1/560 × 5600 years
= 1 × 5600/560 years
= 5600/560 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Donald had to pay $5175 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) How much loan did Karen borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7437.5 to clear it?
(3) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 10% simple interest?
(4) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.
(5) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 6% simple interest?
(6) 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?
(7) Find the amount to be paid if Susan borrowed a sum of $5650 at 8% simple interest for 8 years.
(8) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8740 to clear the loan, then find the time period of the loan.
(9) In how much time a principal of $3050 will amount to $3233 at a simple interest of 2% per annum?
(10) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 3% simple interest?