Question:
Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 7 years.
Correct Answer
$7810
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 6%
Time (t) = 7 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) = $5500 × 6% × 7
= $5500 ×6/100 × 7
= 5500 × 6 × 7/100
= 33000 × 7/100
= 231000/100
= $2310
Thus, Simple Interest = $2310
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 + $2310
= $7810
Thus, Amount to be paid = $7810 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) = 6%
And, Time (t) = 7 years
Thus, Amount (A)
= $5500 + ($5500 × 6% × 7)
= $5500 + ($5500 ×6/100 × 7)
= $5500 + (5500 × 6 × 7/100)
= $5500 + (33000 × 7/100)
= $5500 + (231000/100)
= $5500 + $2310 = $7810
Thus, Amount (A) to be paid = $7810 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 $5500, the simple interest in 1 year
= 6/100 × 5500
= 6 × 5500/100
= 33000/100 = $330
Thus, simple interest for 1 year = $330
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $330 × 7 = $2310
Thus, Simple Interest (SI) = $2310
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $2310
= $7810
Thus, Amount to be paid = $7810 Answer
Similar Questions
(1) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 8% simple interest.
(2) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 5% simple interest?
(3) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 4% simple interest.
(4) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 6% simple interest?
(5) Calculate the amount due if Susan borrowed a sum of $3650 at 6% simple interest for 3 years.
(6) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7208 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 9% simple interest.
(8) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Robert borrowed a sum of $3100 at 2% simple interest for 3 years.
(10) In how much time a principal of $3100 will amount to $3410 at a simple interest of 5% per annum?