Question:
Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 8% simple interest.
Correct Answer
$9540
Solution And Explanation
Solution
Given,
Principal (P) = $5300
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) = $5300 × 8% × 10
= $5300 ×8/100 × 10
= 5300 × 8 × 10/100
= 42400 × 10/100
= 424000/100
= $4240
Thus, Simple Interest = $4240
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 = $5300 + $4240
= $9540
Thus, Amount to be paid = $9540 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 = $5300
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 10 years
Thus, Amount (A)
= $5300 + ($5300 × 8% × 10)
= $5300 + ($5300 ×8/100 × 10)
= $5300 + (5300 × 8 × 10/100)
= $5300 + (42400 × 10/100)
= $5300 + (424000/100)
= $5300 + $4240 = $9540
Thus, Amount (A) to be paid = $9540 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 $5300, the simple interest in 1 year
= 8/100 × 5300
= 8 × 5300/100
= 42400/100 = $424
Thus, simple interest for 1 year = $424
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $424 × 10 = $4240
Thus, Simple Interest (SI) = $4240
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $4240
= $9540
Thus, Amount to be paid = $9540 Answer
Similar Questions
(1) Steven had to pay $4876 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 9% simple interest?
(3) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.
(4) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 6% simple interest?
(5) What amount does James have to pay after 5 years if he takes a loan of $3000 at 9% simple interest?
(6) Find the amount to be paid if Barbara borrowed a sum of $5550 at 8% simple interest for 7 years.
(7) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.
(8) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 8 years.
(10) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 10% simple interest.