Question:
Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.
Correct Answer
$6540.5
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 3%
Time (t) = 9 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% × 9
= $5150 ×3/100 × 9
= 5150 × 3 × 9/100
= 15450 × 9/100
= 139050/100
= $1390.5
Thus, Simple Interest = $1390.5
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 = $5150 + $1390.5
= $6540.5
Thus, Amount to be paid = $6540.5 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 = $5150
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 9 years
Thus, Amount (A)
= $5150 + ($5150 × 3% × 9)
= $5150 + ($5150 ×3/100 × 9)
= $5150 + (5150 × 3 × 9/100)
= $5150 + (15450 × 9/100)
= $5150 + (139050/100)
= $5150 + $1390.5 = $6540.5
Thus, Amount (A) to be paid = $6540.5 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 $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 9 years
= Simple interest for 1 year × 9
= $154.5 × 9 = $1390.5
Thus, Simple Interest (SI) = $1390.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $1390.5
= $6540.5
Thus, Amount to be paid = $6540.5 Answer
Similar Questions
(1) Andrew had to pay $5232 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(2) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 9% simple interest?
(3) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 9% simple interest?
(4) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 7% simple interest?
(5) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8869 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if James borrowed a sum of $5000 at 3% simple interest for 8 years.
(7) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 8% simple interest?
(8) If Joseph borrowed $3700 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 6% simple interest for 3 years.
(10) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 2% simple interest.