Question:
Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 8% simple interest.
Correct Answer
$9900
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 8%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 10
= $5500 ×8/100 × 10
= 5500 × 8 × 10/100
= 44000 × 10/100
= 440000/100
= $4400
Thus, Simple Interest = $4400
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 + $4400
= $9900
Thus, Amount to be paid = $9900 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) = 8%
And, Time (t) = 10 years
Thus, Amount (A)
= $5500 + ($5500 × 8% × 10)
= $5500 + ($5500 ×8/100 × 10)
= $5500 + (5500 × 8 × 10/100)
= $5500 + (44000 × 10/100)
= $5500 + (440000/100)
= $5500 + $4400 = $9900
Thus, Amount (A) to be paid = $9900 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5500, the simple interest in 1 year
= 8/100 × 5500
= 8 × 5500/100
= 44000/100 = $440
Thus, simple interest for 1 year = $440
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $440 × 10 = $4400
Thus, Simple Interest (SI) = $4400
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $4400
= $9900
Thus, Amount to be paid = $9900 Answer
Similar Questions
(1) Calculate the amount due if Jennifer borrowed a sum of $3250 at 3% simple interest for 3 years.
(2) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.
(4) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 7 years.
(5) Find the amount to be paid if Charles borrowed a sum of $5900 at 3% simple interest for 8 years.
(6) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 2% simple interest?
(7) William had to pay $4025 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 3 years.
(9) If Jennifer paid $3770 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.