Question:
Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6664 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $4900
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $6664
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 = $6664 – $4900 = $1764
Thus, Simple Interest = $1764
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 × 1764/4900 × 6
= 176400/29400
= 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) = $4900
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $1764 (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 = 6% of Principal
= 6% of $4900
= 6/100 × 4900
= 6 × 4900/100
= 29400/100 = 294
Thus, simple Interest for 1 year = $294
Now,
∵ If the simple Interest is $294, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/294 years
∴ If the simple Interest is $1764, then the time = 1/294 × 1764 years
= 1 × 1764/294 years
= 1764/294 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Calculate the amount due if Joseph borrowed a sum of $3700 at 5% simple interest for 4 years.
(2) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 2% simple interest?
(3) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 5% per annum?
(4) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 8% simple interest?
(5) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 7% simple interest for 8 years.
(6) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 8 years.
(7) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 8% simple interest?
(8) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 6% simple interest?
(9) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 8 years.
(10) Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 7 years.