Question:
Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.
Correct Answer
$8240
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 6%
Time (t) = 10 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) = $5150 × 6% × 10
= $5150 ×6/100 × 10
= 5150 × 6 × 10/100
= 30900 × 10/100
= 309000/100
= $3090
Thus, Simple Interest = $3090
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 + $3090
= $8240
Thus, Amount to be paid = $8240 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) = 6%
And, Time (t) = 10 years
Thus, Amount (A)
= $5150 + ($5150 × 6% × 10)
= $5150 + ($5150 ×6/100 × 10)
= $5150 + (5150 × 6 × 10/100)
= $5150 + (30900 × 10/100)
= $5150 + (309000/100)
= $5150 + $3090 = $8240
Thus, Amount (A) to be paid = $8240 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 $5150, the simple interest in 1 year
= 6/100 × 5150
= 6 × 5150/100
= 30900/100 = $309
Thus, simple interest for 1 year = $309
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $309 × 10 = $3090
Thus, Simple Interest (SI) = $3090
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $3090
= $8240
Thus, Amount to be paid = $8240 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.
(2) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 4 years.
(3) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $12000 to clear the loan, then find the time period of the loan.
(4) In how much time a principal of $3050 will amount to $3233 at a simple interest of 3% per annum?
(5) Calculate the amount due if Susan borrowed a sum of $3650 at 8% simple interest for 3 years.
(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 4% simple interest for 8 years.
(7) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
(8) Sandra had to pay $4717 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10560 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 9% simple interest.