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) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 7% simple interest?
(2) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6776 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 8 years.
(4) Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 7 years.
(5) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8745 to clear it?
(6) Emily had to pay $5320 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.
(8) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 6% simple interest?
(9) Calculate the amount due if John borrowed a sum of $3200 at 2% simple interest for 3 years.
(10) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.