Question:
Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.
Correct Answer
$9086
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 6%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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) = $5900 × 6% × 9
= $5900 ×6/100 × 9
= 5900 × 6 × 9/100
= 35400 × 9/100
= 318600/100
= $3186
Thus, Simple Interest = $3186
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 = $5900 + $3186
= $9086
Thus, Amount to be paid = $9086 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 = $5900
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 9 years
Thus, Amount (A)
= $5900 + ($5900 × 6% × 9)
= $5900 + ($5900 ×6/100 × 9)
= $5900 + (5900 × 6 × 9/100)
= $5900 + (35400 × 9/100)
= $5900 + (318600/100)
= $5900 + $3186 = $9086
Thus, Amount (A) to be paid = $9086 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5900, the simple interest in 1 year
= 6/100 × 5900
= 6 × 5900/100
= 35400/100 = $354
Thus, simple interest for 1 year = $354
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $354 × 9 = $3186
Thus, Simple Interest (SI) = $3186
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $3186
= $9086
Thus, Amount to be paid = $9086 Answer
Similar Questions
(1) Find the amount to be paid if Jessica borrowed a sum of $5750 at 7% simple interest for 7 years.
(2) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 2% simple interest?
(3) Calculate the amount due if Barbara borrowed a sum of $3550 at 2% simple interest for 4 years.
(4) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.
(5) How much loan did Paul borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8375 to clear it?
(6) Calculate the amount due if Linda borrowed a sum of $3350 at 5% simple interest for 4 years.
(7) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 7% simple interest for 3 years.
(8) Find the amount to be paid if Richard borrowed a sum of $5600 at 2% simple interest for 8 years.
(9) In how much time a principal of $3100 will amount to $3596 at a simple interest of 4% per annum?
(10) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.