Question:
What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 3% simple interest?
Correct Answer
$3622.5
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 3%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 5
= $3150 ×3/100 × 5
= 3150 × 3 × 5/100
= 9450 × 5/100
= 47250/100
= $472.5
Thus, Simple Interest = $472.5
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 + $472.5
= $3622.5
Thus, Amount to be paid = $3622.5 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) = 3%
And, Time (t) = 5 years
Thus, Amount (A)
= $3150 + ($3150 × 3% × 5)
= $3150 + ($3150 ×3/100 × 5)
= $3150 + (3150 × 3 × 5/100)
= $3150 + (9450 × 5/100)
= $3150 + (47250/100)
= $3150 + $472.5 = $3622.5
Thus, Amount (A) to be paid = $3622.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $3150, the simple interest in 1 year
= 3/100 × 3150
= 3 × 3150/100
= 9450/100 = $94.5
Thus, simple interest for 1 year = $94.5
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $94.5 × 5 = $472.5
Thus, Simple Interest (SI) = $472.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $472.5
= $3622.5
Thus, Amount to be paid = $3622.5 Answer
Similar Questions
(1) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 3 years.
(2) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Mary borrowed a sum of $5050 at 4% simple interest for 7 years.
(4) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.
(5) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $6468 to clear the loan, then find the time period of the loan.
(6) How much loan did James borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6250 to clear it?
(7) Calculate the amount due if Richard borrowed a sum of $3600 at 8% simple interest for 3 years.
(8) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $11152 to clear the loan, then find the time period of the loan.
(9) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.
(10) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 2% simple interest?