Question:
Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6200
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $10664
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 = $10664 – $6200 = $4464
Thus, Simple Interest = $4464
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 × 4464/6200 × 8
= 446400/49600
= 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) = $6200
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $4464 (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 $6200
= 8/100 × 6200
= 8 × 6200/100
= 49600/100 = 496
Thus, simple Interest for 1 year = $496
Now,
∵ If the simple Interest is $496, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/496 years
∴ If the simple Interest is $4464, then the time = 1/496 × 4464 years
= 1 × 4464/496 years
= 4464/496 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Thomas had to pay $4142 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(2) Linda had to pay $3752 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 10% simple interest?
(4) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 10% simple interest?
(5) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.
(6) How much loan did Jacob borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8800 to clear it?
(7) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 10% simple interest.
(8) What amount will be due after 2 years if David borrowed a sum of $3200 at a 7% simple interest?
(9) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.