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) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6216 to clear the loan, then find the time period of the loan.
(2) What amount does William have to pay after 5 years if he takes a loan of $3500 at 4% simple interest?
(3) How much loan did Sandra borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7417.5 to clear it?
(4) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9020 to clear the loan, then find the time period of the loan.
(5) If Patricia paid $3528 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7498 to clear the loan, then find the time period of the loan.
(7) If Karen paid $4424 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 5% simple interest for 3 years.
(9) What amount will be due after 2 years if John borrowed a sum of $3100 at a 9% simple interest?
(10) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.