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) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.
(2) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 6% simple interest for 4 years.
(4) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.
(5) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.
(6) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 3 years.
(8) What amount does John have to pay after 6 years if he takes a loan of $3200 at 4% simple interest?
(9) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.
(10) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 4% simple interest?