Question:
Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 4 years.
Correct Answer
$4260
Solution And Explanation
Solution
Given,
Principal (P) = $3550
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) = $3550 × 5% × 4
= $3550 ×5/100 × 4
= 3550 × 5 × 4/100
= 17750 × 4/100
= 71000/100
= $710
Thus, Simple Interest = $710
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 + $710
= $4260
Thus, Amount to be paid = $4260 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) = 5%
And, Time (t) = 4 years
Thus, Amount (A)
= $3550 + ($3550 × 5% × 4)
= $3550 + ($3550 ×5/100 × 4)
= $3550 + (3550 × 5 × 4/100)
= $3550 + (17750 × 4/100)
= $3550 + (71000/100)
= $3550 + $710 = $4260
Thus, Amount (A) to be paid = $4260 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 $3550, the simple interest in 1 year
= 5/100 × 3550
= 5 × 3550/100
= 17750/100 = $177.5
Thus, simple interest for 1 year = $177.5
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $177.5 × 4 = $710
Thus, Simple Interest (SI) = $710
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3550 + $710
= $4260
Thus, Amount to be paid = $4260 Answer
Similar Questions
(1) Kimberly had to pay $5068.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(2) What amount does John have to pay after 5 years if he takes a loan of $3200 at 2% simple interest?
(3) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 7% simple interest?
(4) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.
(5) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9955 to clear the loan, then find the time period of the loan.
(6) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 8% simple interest?
(7) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9184 to clear the loan, then find the time period of the loan.
(8) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 2% simple interest for 3 years.
(10) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 3% per annum?