Question:
What amount does William have to pay after 6 years if he takes a loan of $3500 at 5% simple interest?
Correct Answer
$4550
Solution And Explanation
Solution
Given,
Principal (P) = $3500
Rate of Simple Interest (SI) = 5%
Time (t) = 6 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) = $3500 × 5% × 6
= $3500 ×5/100 × 6
= 3500 × 5 × 6/100
= 17500 × 6/100
= 105000/100
= $1050
Thus, Simple Interest = $1050
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 = $3500 + $1050
= $4550
Thus, Amount to be paid = $4550 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 = $3500
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 6 years
Thus, Amount (A)
= $3500 + ($3500 × 5% × 6)
= $3500 + ($3500 ×5/100 × 6)
= $3500 + (3500 × 5 × 6/100)
= $3500 + (17500 × 6/100)
= $3500 + (105000/100)
= $3500 + $1050 = $4550
Thus, Amount (A) to be paid = $4550 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 $3500, the simple interest in 1 year
= 5/100 × 3500
= 5 × 3500/100
= 17500/100 = $175
Thus, simple interest for 1 year = $175
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $175 × 6 = $1050
Thus, Simple Interest (SI) = $1050
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3500 + $1050
= $4550
Thus, Amount to be paid = $4550 Answer
Similar Questions
(1) In how much time a principal of $3150 will amount to $3402 at a simple interest of 4% per annum?
(2) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9943 to clear the loan, then find the time period of the loan.
(3) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 5% simple interest?
(4) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9834 to clear the loan, then find the time period of the loan.
(5) Michael had to pay $3696 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11403 to clear the loan, then find the time period of the loan.
(7) Michelle had to pay $5692.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) Calculate the amount due if Thomas borrowed a sum of $3800 at 10% simple interest for 4 years.
(9) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 6% simple interest.
(10) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 4% simple interest?