Question:
Find the amount to be paid if Karen borrowed a sum of $5950 at 6% simple interest for 7 years.
Correct Answer
$8449
Solution And Explanation
Solution
Given,
Principal (P) = $5950
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) = $5950 × 6% × 7
= $5950 ×6/100 × 7
= 5950 × 6 × 7/100
= 35700 × 7/100
= 249900/100
= $2499
Thus, Simple Interest = $2499
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 = $5950 + $2499
= $8449
Thus, Amount to be paid = $8449 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 = $5950
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 7 years
Thus, Amount (A)
= $5950 + ($5950 × 6% × 7)
= $5950 + ($5950 ×6/100 × 7)
= $5950 + (5950 × 6 × 7/100)
= $5950 + (35700 × 7/100)
= $5950 + (249900/100)
= $5950 + $2499 = $8449
Thus, Amount (A) to be paid = $8449 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 $5950, the simple interest in 1 year
= 6/100 × 5950
= 6 × 5950/100
= 35700/100 = $357
Thus, simple interest for 1 year = $357
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $357 × 7 = $2499
Thus, Simple Interest (SI) = $2499
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $2499
= $8449
Thus, Amount to be paid = $8449 Answer
Similar Questions
(1) What amount does William have to pay after 6 years if he takes a loan of $3500 at 2% simple interest?
(2) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9800 to clear the loan, then find the time period of the loan.
(3) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8296 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Christopher borrowed a sum of $4000 at 4% simple interest for 4 years.
(5) How much loan did Mary borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6312.5 to clear it?
(6) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 3% simple interest.
(7) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 9% simple interest?
(8) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 6% simple interest?
(9) In how much time a principal of $3000 will amount to $3300 at a simple interest of 5% 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.