Question:
Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $10498 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $10498
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 = $10498 – $5800 = $4698
Thus, Simple Interest = $4698
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 × 4698/5800 × 9
= 469800/52200
= 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) = $5800
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $4698 (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 = 9% of Principal
= 9% of $5800
= 9/100 × 5800
= 9 × 5800/100
= 52200/100 = 522
Thus, simple Interest for 1 year = $522
Now,
∵ If the simple Interest is $522, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/522 years
∴ If the simple Interest is $4698, then the time = 1/522 × 4698 years
= 1 × 4698/522 years
= 4698/522 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Emily had to pay $5035 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 8% simple interest?
(3) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 3% simple interest?
(4) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 2% simple interest?
(5) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 2% simple interest for 7 years.
(6) Calculate the amount due if Charles borrowed a sum of $3900 at 9% simple interest for 3 years.
(7) Calculate the amount due if Linda borrowed a sum of $3350 at 8% simple interest for 4 years.
(8) What amount does William have to pay after 6 years if he takes a loan of $3500 at 8% simple interest?
(9) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.
(10) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $9940 to clear the loan, then find the time period of the loan.