Question:
Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $4900
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $7987
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 = $7987 – $4900 = $3087
Thus, Simple Interest = $3087
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 × 3087/4900 × 7
= 308700/34300
= 9 years (using formula)
Thus, Time (T) = 9 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) = $4900
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $3087 (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 $4900
= 7/100 × 4900
= 7 × 4900/100
= 34300/100 = 343
Thus, simple Interest for 1 year = $343
Now,
∵ If the simple Interest is $343, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/343 years
∴ If the simple Interest is $3087, then the time = 1/343 × 3087 years
= 1 × 3087/343 years
= 3087/343 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 4% simple interest.
(2) How much loan did Timothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8510 to clear it?
(3) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.
(4) If Sandra paid $4984 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 2% simple interest.
(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 3 years.
(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 7 years.
(8) Joseph had to pay $4144 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.
(10) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 2% simple interest?