Question:
Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 5% simple interest.
Correct Answer
$8047.5
Solution And Explanation
Solution
Given,
Principal (P) = $5550
Rate of Simple Interest (SI) = 5%
Time (t) = 9 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) = $5550 × 5% × 9
= $5550 ×5/100 × 9
= 5550 × 5 × 9/100
= 27750 × 9/100
= 249750/100
= $2497.5
Thus, Simple Interest = $2497.5
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 = $5550 + $2497.5
= $8047.5
Thus, Amount to be paid = $8047.5 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 = $5550
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 9 years
Thus, Amount (A)
= $5550 + ($5550 × 5% × 9)
= $5550 + ($5550 ×5/100 × 9)
= $5550 + (5550 × 5 × 9/100)
= $5550 + (27750 × 9/100)
= $5550 + (249750/100)
= $5550 + $2497.5 = $8047.5
Thus, Amount (A) to be paid = $8047.5 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 $5550, the simple interest in 1 year
= 5/100 × 5550
= 5 × 5550/100
= 27750/100 = $277.5
Thus, simple interest for 1 year = $277.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $277.5 × 9 = $2497.5
Thus, Simple Interest (SI) = $2497.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5550 + $2497.5
= $8047.5
Thus, Amount to be paid = $8047.5 Answer
Similar Questions
(1) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 6% simple interest for 8 years.
(2) In how much time a principal of $3000 will amount to $3750 at a simple interest of 5% per annum?
(3) What amount does James have to pay after 6 years if he takes a loan of $3000 at 8% simple interest?
(4) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.
(5) What amount does William have to pay after 5 years if he takes a loan of $3500 at 3% simple interest?
(6) If Charles borrowed $3900 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 3 years.
(8) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7242 to clear the loan, then find the time period of the loan.
(9) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 4% simple interest?
(10) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 9% simple interest?