Question:
Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.
Correct Answer
$8858
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 8%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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) = $5150 × 8% × 9
= $5150 ×8/100 × 9
= 5150 × 8 × 9/100
= 41200 × 9/100
= 370800/100
= $3708
Thus, Simple Interest = $3708
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 = $5150 + $3708
= $8858
Thus, Amount to be paid = $8858 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 = $5150
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 9 years
Thus, Amount (A)
= $5150 + ($5150 × 8% × 9)
= $5150 + ($5150 ×8/100 × 9)
= $5150 + (5150 × 8 × 9/100)
= $5150 + (41200 × 9/100)
= $5150 + (370800/100)
= $5150 + $3708 = $8858
Thus, Amount (A) to be paid = $8858 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5150, the simple interest in 1 year
= 8/100 × 5150
= 8 × 5150/100
= 41200/100 = $412
Thus, simple interest for 1 year = $412
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $412 × 9 = $3708
Thus, Simple Interest (SI) = $3708
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $3708
= $8858
Thus, Amount to be paid = $8858 Answer
Similar Questions
(1) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 7% simple interest.
(2) Find the amount to be paid if Linda borrowed a sum of $5350 at 3% simple interest for 8 years.
(3) Nancy had to pay $4523.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 7% simple interest.
(5) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.
(7) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.
(8) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 10% simple interest?
(9) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 4 years.
(10) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.