Question:
What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 2% simple interest?
Correct Answer
$3465
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 2%
Time (t) = 5 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% × 5
= $3150 ×2/100 × 5
= 3150 × 2 × 5/100
= 6300 × 5/100
= 31500/100
= $315
Thus, Simple Interest = $315
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 + $315
= $3465
Thus, Amount to be paid = $3465 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) = 5 years
Thus, Amount (A)
= $3150 + ($3150 × 2% × 5)
= $3150 + ($3150 ×2/100 × 5)
= $3150 + (3150 × 2 × 5/100)
= $3150 + (6300 × 5/100)
= $3150 + (31500/100)
= $3150 + $315 = $3465
Thus, Amount (A) to be paid = $3465 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 5 years
= Simple interest for 1 year × 5
= $63 × 5 = $315
Thus, Simple Interest (SI) = $315
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $315
= $3465
Thus, Amount to be paid = $3465 Answer
Similar Questions
(1) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10064 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 7% simple interest?
(3) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9387 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 7 years.
(5) Jessica had to pay $3975 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 10% simple interest?
(7) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 4 years.
(8) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 9% simple interest?
(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 4 years.
(10) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.