Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 5% simple interest for 8 years.
Correct Answer
$7420
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 5%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 8
= $5300 ×5/100 × 8
= 5300 × 5 × 8/100
= 26500 × 8/100
= 212000/100
= $2120
Thus, Simple Interest = $2120
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 + $2120
= $7420
Thus, Amount to be paid = $7420 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) = 5%
And, Time (t) = 8 years
Thus, Amount (A)
= $5300 + ($5300 × 5% × 8)
= $5300 + ($5300 ×5/100 × 8)
= $5300 + (5300 × 5 × 8/100)
= $5300 + (26500 × 8/100)
= $5300 + (212000/100)
= $5300 + $2120 = $7420
Thus, Amount (A) to be paid = $7420 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5300, the simple interest in 1 year
= 5/100 × 5300
= 5 × 5300/100
= 26500/100 = $265
Thus, simple interest for 1 year = $265
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $265 × 8 = $2120
Thus, Simple Interest (SI) = $2120
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $2120
= $7420
Thus, Amount to be paid = $7420 Answer
Similar Questions
(1) Calculate the amount due if Susan borrowed a sum of $3650 at 2% simple interest for 3 years.
(2) In how much time a principal of $3100 will amount to $3565 at a simple interest of 3% per annum?
(3) What amount does William have to pay after 5 years if he takes a loan of $3500 at 3% simple interest?
(4) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 7% simple interest?
(5) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.
(6) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7897 to clear the loan, then find the time period of the loan.
(7) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7242 to clear the loan, then find the time period of the loan.
(8) Matthew had to pay $4830 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.
(10) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.