Question:
Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 8 years.
Correct Answer
$8580
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 7%
Time (t) = 8 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) = $5500 × 7% × 8
= $5500 ×7/100 × 8
= 5500 × 7 × 8/100
= 38500 × 8/100
= 308000/100
= $3080
Thus, Simple Interest = $3080
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 = $5500 + $3080
= $8580
Thus, Amount to be paid = $8580 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 = $5500
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 8 years
Thus, Amount (A)
= $5500 + ($5500 × 7% × 8)
= $5500 + ($5500 ×7/100 × 8)
= $5500 + (5500 × 7 × 8/100)
= $5500 + (38500 × 8/100)
= $5500 + (308000/100)
= $5500 + $3080 = $8580
Thus, Amount (A) to be paid = $8580 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 $5500, the simple interest in 1 year
= 7/100 × 5500
= 7 × 5500/100
= 38500/100 = $385
Thus, simple interest for 1 year = $385
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $385 × 8 = $3080
Thus, Simple Interest (SI) = $3080
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $3080
= $8580
Thus, Amount to be paid = $8580 Answer
Similar Questions
(1) James had to pay $3450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.
(3) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 8 years.
(5) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 8 years.
(6) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 6% simple interest.
(7) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 6% simple interest?
(8) Elizabeth had to pay $3657 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 7 years.
(10) Find the amount to be paid if Susan borrowed a sum of $5650 at 4% simple interest for 7 years.