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) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.
(2) How much loan did Emily borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7425 to clear it?
(3) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $10540 to clear the loan, then find the time period of the loan.
(4) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 8% simple interest?
(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 7 years.
(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 8% simple interest for 8 years.
(7) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.
(8) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.
(9) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.
(10) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.