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) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 5% simple interest.
(3) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 5% simple interest?
(4) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.
(5) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.
(6) If Anthony paid $5160 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.
(8) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.
(10) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.