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) Calculate the amount due if Jessica borrowed a sum of $3750 at 2% simple interest for 4 years.
(2) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 7 years.
(4) 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?
(5) Lisa had to pay $4536 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.
(7) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 5% simple interest?
(8) Margaret had to pay $5002.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) If Elizabeth paid $3726 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12308 to clear the loan, then find the time period of the loan.