Question:
Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.
Correct Answer
$8755
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 7%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 10
= $5150 ×7/100 × 10
= 5150 × 7 × 10/100
= 36050 × 10/100
= 360500/100
= $3605
Thus, Simple Interest = $3605
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 + $3605
= $8755
Thus, Amount to be paid = $8755 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) = 7%
And, Time (t) = 10 years
Thus, Amount (A)
= $5150 + ($5150 × 7% × 10)
= $5150 + ($5150 ×7/100 × 10)
= $5150 + (5150 × 7 × 10/100)
= $5150 + (36050 × 10/100)
= $5150 + (360500/100)
= $5150 + $3605 = $8755
Thus, Amount (A) to be paid = $8755 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5150, the simple interest in 1 year
= 7/100 × 5150
= 7 × 5150/100
= 36050/100 = $360.5
Thus, simple interest for 1 year = $360.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $360.5 × 10 = $3605
Thus, Simple Interest (SI) = $3605
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $3605
= $8755
Thus, Amount to be paid = $8755 Answer
Similar Questions
(1) Daniel had to pay $4592 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 9% simple interest?
(3) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 8 years.
(4) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 9% simple interest?
(5) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10988 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 4 years.
(7) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 9% simple interest?
(8) Find the amount to be paid if David borrowed a sum of $5400 at 9% simple interest for 8 years.
(9) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.
(10) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 7 years.