Question:
Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.
Correct Answer
$6077
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 2%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 9
= $5150 ×2/100 × 9
= 5150 × 2 × 9/100
= 10300 × 9/100
= 92700/100
= $927
Thus, Simple Interest = $927
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 + $927
= $6077
Thus, Amount to be paid = $6077 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) = 2%
And, Time (t) = 9 years
Thus, Amount (A)
= $5150 + ($5150 × 2% × 9)
= $5150 + ($5150 ×2/100 × 9)
= $5150 + (5150 × 2 × 9/100)
= $5150 + (10300 × 9/100)
= $5150 + (92700/100)
= $5150 + $927 = $6077
Thus, Amount (A) to be paid = $6077 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5150, the simple interest in 1 year
= 2/100 × 5150
= 2 × 5150/100
= 10300/100 = $103
Thus, simple interest for 1 year = $103
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $103 × 9 = $927
Thus, Simple Interest (SI) = $927
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $927
= $6077
Thus, Amount to be paid = $6077 Answer
Similar Questions
(1) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 8% simple interest.
(2) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 8 years.
(4) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Linda borrowed a sum of $5350 at 10% simple interest for 7 years.
(6) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 9% simple interest?
(7) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 2% simple interest.
(8) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 7 years.
(9) Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 4 years.
(10) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6258 to clear the loan, then find the time period of the loan.