Question:
Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 8 years.
Correct Answer
$6386
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 3%
Time (t) = 8 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% × 8
= $5150 ×3/100 × 8
= 5150 × 3 × 8/100
= 15450 × 8/100
= 123600/100
= $1236
Thus, Simple Interest = $1236
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 + $1236
= $6386
Thus, Amount to be paid = $6386 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) = 8 years
Thus, Amount (A)
= $5150 + ($5150 × 3% × 8)
= $5150 + ($5150 ×3/100 × 8)
= $5150 + (5150 × 3 × 8/100)
= $5150 + (15450 × 8/100)
= $5150 + (123600/100)
= $5150 + $1236 = $6386
Thus, Amount (A) to be paid = $6386 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 8 years
= Simple interest for 1 year × 8
= $154.5 × 8 = $1236
Thus, Simple Interest (SI) = $1236
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $1236
= $6386
Thus, Amount to be paid = $6386 Answer
Similar Questions
(1) How much loan did Ryan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9480 to clear it?
(2) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 7% simple interest?
(3) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 5% simple interest.
(4) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 10% simple interest.
(5) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 10% simple interest?
(6) Find the amount to be paid if Jessica borrowed a sum of $5750 at 8% simple interest for 7 years.
(7) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.
(8) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 4 years.
(9) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.
(10) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5680 to clear the loan, then find the time period of the loan.