Question:
Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 4 years.
Correct Answer
$4620
Solution And Explanation
Solution
Given,
Principal (P) = $3850
Rate of Simple Interest (SI) = 5%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% per annum.
Method (1) Using Formula
Calculation of Simple Interest
Formula to Calculate Simple Interest
Simple Interest (SI) = Principal × Rate × Time
Thus, Simple Interest (SI) = $3850 × 5% × 4
= $3850 ×5/100 × 4
= 3850 × 5 × 4/100
= 19250 × 4/100
= 77000/100
= $770
Thus, Simple Interest = $770
Calculation of Amount
The total money paid to the lender by a borrower is called the Amount.
In other words, sum of priciple and interest is called the Amount.
Formula to Calculate the Amount
Amount = Principal + Interest
Thus, Amount = $3850 + $770
= $4620
Thus, Amount to be paid = $4620 Answer
Method (2)
Calculation of Amount when Principal, Rate of Simple Interest and Time are given
Calculation of Amount directly using Principal, SI, and Time
Formula to calculate the Amount
Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)
⇒ A = P + PRT
Here in the question, P = $3850
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 4 years
Thus, Amount (A)
= $3850 + ($3850 × 5% × 4)
= $3850 + ($3850 ×5/100 × 4)
= $3850 + (3850 × 5 × 4/100)
= $3850 + (19250 × 4/100)
= $3850 + (77000/100)
= $3850 + $770 = $4620
Thus, Amount (A) to be paid = $4620 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $3850, the simple interest in 1 year
= 5/100 × 3850
= 5 × 3850/100
= 19250/100 = $192.5
Thus, simple interest for 1 year = $192.5
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $192.5 × 4 = $770
Thus, Simple Interest (SI) = $770
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3850 + $770
= $4620
Thus, Amount to be paid = $4620 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 2% simple interest.
(2) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 3 years.
(3) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 2% simple interest.
(4) What amount does James have to pay after 6 years if he takes a loan of $3000 at 8% simple interest?
(5) In how much time a principal of $3100 will amount to $3379 at a simple interest of 3% per annum?
(6) If Kimberly paid $5580 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 7 years.
(8) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9800 to clear the loan, then find the time period of the loan.
(9) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.
(10) Nancy had to pay $4399 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.