Question:
Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.
Correct Answer
$6695
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 3%
Time (t) = 10 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) = $5150 × 3% × 10
= $5150 ×3/100 × 10
= 5150 × 3 × 10/100
= 15450 × 10/100
= 154500/100
= $1545
Thus, Simple Interest = $1545
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 + $1545
= $6695
Thus, Amount to be paid = $6695 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) = 3%
And, Time (t) = 10 years
Thus, Amount (A)
= $5150 + ($5150 × 3% × 10)
= $5150 + ($5150 ×3/100 × 10)
= $5150 + (5150 × 3 × 10/100)
= $5150 + (15450 × 10/100)
= $5150 + (154500/100)
= $5150 + $1545 = $6695
Thus, Amount (A) to be paid = $6695 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 $5150, the simple interest in 1 year
= 3/100 × 5150
= 3 × 5150/100
= 15450/100 = $154.5
Thus, simple interest for 1 year = $154.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $154.5 × 10 = $1545
Thus, Simple Interest (SI) = $1545
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $1545
= $6695
Thus, Amount to be paid = $6695 Answer
Similar Questions
(1) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 3 years.
(2) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.
(3) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 3% simple interest?
(4) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 3% simple interest for 7 years.
(5) What amount does William have to pay after 6 years if he takes a loan of $3500 at 4% simple interest?
(6) If Joseph paid $3996 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 4% simple interest.
(8) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.
(9) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.
(10) If John paid $3712 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.