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) How much loan did Deborah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8567.5 to clear it?
(2) What amount will be due after 2 years if David borrowed a sum of $3200 at a 5% simple interest?
(3) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 7 years.
(4) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9562.5 to clear it?
(5) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 8% simple interest?
(7) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.
(8) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 5% simple interest?
(9) Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 8 years.
(10) How much loan did Ryan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9085 to clear it?