Question:
What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 3% simple interest?
Correct Answer
$4082.5
Solution And Explanation
Solution
Given,
Principal (P) = $3550
Rate of Simple Interest (SI) = 3%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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) = $3550 × 3% × 5
= $3550 ×3/100 × 5
= 3550 × 3 × 5/100
= 10650 × 5/100
= 53250/100
= $532.5
Thus, Simple Interest = $532.5
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 = $3550 + $532.5
= $4082.5
Thus, Amount to be paid = $4082.5 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 = $3550
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 5 years
Thus, Amount (A)
= $3550 + ($3550 × 3% × 5)
= $3550 + ($3550 ×3/100 × 5)
= $3550 + (3550 × 3 × 5/100)
= $3550 + (10650 × 5/100)
= $3550 + (53250/100)
= $3550 + $532.5 = $4082.5
Thus, Amount (A) to be paid = $4082.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $3550, the simple interest in 1 year
= 3/100 × 3550
= 3 × 3550/100
= 10650/100 = $106.5
Thus, simple interest for 1 year = $106.5
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $106.5 × 5 = $532.5
Thus, Simple Interest (SI) = $532.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3550 + $532.5
= $4082.5
Thus, Amount to be paid = $4082.5 Answer
Similar Questions
(1) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 10% simple interest?
(2) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 4% simple interest?
(3) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 7 years.
(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 7% simple interest for 7 years.
(5) David had to pay $3604 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.
(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 after 10 years if John borrowed a sum of $5200 at a rate of 9% simple interest.
(9) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8140 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.