Question:
What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 2% simple interest?
Correct Answer
$3528
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 2%
Time (t) = 6 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) = $3150 × 2% × 6
= $3150 ×2/100 × 6
= 3150 × 2 × 6/100
= 6300 × 6/100
= 37800/100
= $378
Thus, Simple Interest = $378
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 = $3150 + $378
= $3528
Thus, Amount to be paid = $3528 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 = $3150
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 6 years
Thus, Amount (A)
= $3150 + ($3150 × 2% × 6)
= $3150 + ($3150 ×2/100 × 6)
= $3150 + (3150 × 2 × 6/100)
= $3150 + (6300 × 6/100)
= $3150 + (37800/100)
= $3150 + $378 = $3528
Thus, Amount (A) to be paid = $3528 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 $3150, the simple interest in 1 year
= 2/100 × 3150
= 2 × 3150/100
= 6300/100 = $63
Thus, simple interest for 1 year = $63
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $63 × 6 = $378
Thus, Simple Interest (SI) = $378
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $378
= $3528
Thus, Amount to be paid = $3528 Answer
Similar Questions
(1) What amount does William have to pay after 6 years if he takes a loan of $3500 at 3% simple interest?
(2) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 4 years.
(4) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Robert borrowed a sum of $5100 at 6% simple interest for 7 years.
(6) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 5% simple interest.
(7) Richard had to pay $3816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 9% simple interest?
(9) Calculate the amount due if William borrowed a sum of $3500 at 4% simple interest for 3 years.
(10) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $10920 to clear the loan, then find the time period of the loan.