Question:
Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $11480 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $7000
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $11480
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 = $11480 – $7000 = $4480
Thus, Simple Interest = $4480
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 × 4480/7000 × 8
= 448000/56000
= 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) = $7000
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $4480 (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 $4480, then the time = 1/560 × 4480 years
= 1 × 4480/560 years
= 4480/560 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.
(2) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(3) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 5% simple interest?
(4) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 3 years.
(5) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 6% simple interest?
(6) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 5% simple interest?
(7) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7072 to clear the loan, then find the time period of the loan.
(8) In how much time a principal of $3150 will amount to $3780 at a simple interest of 4% per annum?
(9) In how much time a principal of $3050 will amount to $3294 at a simple interest of 4% per annum?
(10) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 10% simple interest.