Question:
Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.
Correct Answer
$6077
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 2%
Time (t) = 9 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) = $5150 × 2% × 9
= $5150 ×2/100 × 9
= 5150 × 2 × 9/100
= 10300 × 9/100
= 92700/100
= $927
Thus, Simple Interest = $927
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 + $927
= $6077
Thus, Amount to be paid = $6077 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) = 2%
And, Time (t) = 9 years
Thus, Amount (A)
= $5150 + ($5150 × 2% × 9)
= $5150 + ($5150 ×2/100 × 9)
= $5150 + (5150 × 2 × 9/100)
= $5150 + (10300 × 9/100)
= $5150 + (92700/100)
= $5150 + $927 = $6077
Thus, Amount (A) to be paid = $6077 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 $5150, the simple interest in 1 year
= 2/100 × 5150
= 2 × 5150/100
= 10300/100 = $103
Thus, simple interest for 1 year = $103
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $103 × 9 = $927
Thus, Simple Interest (SI) = $927
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $927
= $6077
Thus, Amount to be paid = $6077 Answer
Similar Questions
(1) If John paid $3456 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) Joseph had to pay $3922 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(3) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.
(4) How much loan did Paul borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7705 to clear it?
(5) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 4% simple interest?
(6) If Donna paid $5626 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 5% simple interest.
(8) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 6% simple interest?
(9) Calculate the amount due if James borrowed a sum of $3000 at 10% simple interest for 3 years.
(10) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 8 years.