Question:
Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 8% simple interest.
Correct Answer
$9632
Solution And Explanation
Solution
Given,
Principal (P) = $5600
Rate of Simple Interest (SI) = 8%
Time (t) = 9 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) = $5600 × 8% × 9
= $5600 ×8/100 × 9
= 5600 × 8 × 9/100
= 44800 × 9/100
= 403200/100
= $4032
Thus, Simple Interest = $4032
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 = $5600 + $4032
= $9632
Thus, Amount to be paid = $9632 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 = $5600
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 9 years
Thus, Amount (A)
= $5600 + ($5600 × 8% × 9)
= $5600 + ($5600 ×8/100 × 9)
= $5600 + (5600 × 8 × 9/100)
= $5600 + (44800 × 9/100)
= $5600 + (403200/100)
= $5600 + $4032 = $9632
Thus, Amount (A) to be paid = $9632 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 $5600, the simple interest in 1 year
= 8/100 × 5600
= 8 × 5600/100
= 44800/100 = $448
Thus, simple interest for 1 year = $448
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $448 × 9 = $4032
Thus, Simple Interest (SI) = $4032
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5600 + $4032
= $9632
Thus, Amount to be paid = $9632 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.
(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 8 years.
(3) How much loan did Mary borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5807.5 to clear it?
(4) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
(5) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.
(6) In how much time a principal of $3200 will amount to $3680 at a simple interest of 5% per annum?
(7) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.
(8) In how much time a principal of $3100 will amount to $3565 at a simple interest of 3% per annum?
(9) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.
(10) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 3% simple interest?