Question:
Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 4% simple interest.
Correct Answer
$7004
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 4%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 9
= $5150 ×4/100 × 9
= 5150 × 4 × 9/100
= 20600 × 9/100
= 185400/100
= $1854
Thus, Simple Interest = $1854
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 + $1854
= $7004
Thus, Amount to be paid = $7004 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) = 4%
And, Time (t) = 9 years
Thus, Amount (A)
= $5150 + ($5150 × 4% × 9)
= $5150 + ($5150 ×4/100 × 9)
= $5150 + (5150 × 4 × 9/100)
= $5150 + (20600 × 9/100)
= $5150 + (185400/100)
= $5150 + $1854 = $7004
Thus, Amount (A) to be paid = $7004 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5150, the simple interest in 1 year
= 4/100 × 5150
= 4 × 5150/100
= 20600/100 = $206
Thus, simple interest for 1 year = $206
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $206 × 9 = $1854
Thus, Simple Interest (SI) = $1854
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $1854
= $7004
Thus, Amount to be paid = $7004 Answer
Similar Questions
(1) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 6% simple interest?
(2) Calculate the amount due if Thomas borrowed a sum of $3800 at 6% simple interest for 4 years.
(3) How much loan did Kevin borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8520 to clear it?
(4) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 4 years.
(5) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.
(6) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 7% simple interest?
(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 4 years.
(8) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 3 years.
(9) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 6% simple interest.
(10) Calculate the amount due if Mary borrowed a sum of $3050 at 4% simple interest for 4 years.