Question:
( 1 of 10 ) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.
(A) 4050
(B) 4051
(C) 4052
(D) 2025.5
You selected
9
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $6200
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $8804
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 = $8804 – $6200 = $2604
Thus, Simple Interest = $2604
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 × 2604/6200 × 7
= 260400/43400
= 6 years (using formula)
Thus, Time (T) = 6 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) = 7% per annum
Simple Interest = $2604 (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 $6200
= 7/100 × 6200
= 7 × 6200/100
= 43400/100 = 434
Thus, simple Interest for 1 year = $434
Now,
∵ If the simple Interest is $434, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/434 years
∴ If the simple Interest is $2604, then the time = 1/434 × 2604 years
= 1 × 2604/434 years
= 2604/434 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) How much loan did George borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8395 to clear it?
(2) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 7% simple interest.
(3) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 10% simple interest?
(4) How much loan did Michelle borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8687.5 to clear it?
(5) Find the amount to be paid if Thomas borrowed a sum of $5800 at 3% simple interest for 8 years.
(6) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(7) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(8) What amount does William have to pay after 6 years if he takes a loan of $3500 at 7% simple interest?
(9) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7498 to clear the loan, then find the time period of the loan.
(10) What amount does William have to pay after 5 years if he takes a loan of $3500 at 5% simple interest?