Question:
Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 8 years.
Correct Answer
$8214
Solution And Explanation
Solution
Given,
Principal (P) = $5550
Rate of Simple Interest (SI) = 6%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 8
= $5550 ×6/100 × 8
= 5550 × 6 × 8/100
= 33300 × 8/100
= 266400/100
= $2664
Thus, Simple Interest = $2664
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 + $2664
= $8214
Thus, Amount to be paid = $8214 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) = 6%
And, Time (t) = 8 years
Thus, Amount (A)
= $5550 + ($5550 × 6% × 8)
= $5550 + ($5550 ×6/100 × 8)
= $5550 + (5550 × 6 × 8/100)
= $5550 + (33300 × 8/100)
= $5550 + (266400/100)
= $5550 + $2664 = $8214
Thus, Amount (A) to be paid = $8214 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5550, the simple interest in 1 year
= 6/100 × 5550
= 6 × 5550/100
= 33300/100 = $333
Thus, simple interest for 1 year = $333
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $333 × 8 = $2664
Thus, Simple Interest (SI) = $2664
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5550 + $2664
= $8214
Thus, Amount to be paid = $8214 Answer
Similar Questions
(1) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(2) What amount does David have to pay after 6 years if he takes a loan of $3400 at 4% simple interest?
(3) In how much time a principal of $3100 will amount to $3348 at a simple interest of 2% per annum?
(4) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 6% simple interest?
(5) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.
(6) Thomas had to pay $4142 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) Calculate the amount due if James borrowed a sum of $3000 at 8% simple interest for 3 years.
(8) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 8% simple interest?
(9) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 8 years.
(10) What amount does William have to pay after 5 years if he takes a loan of $3500 at 8% simple interest?