Question:
What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 8% simple interest?
Correct Answer
$5530
Solution And Explanation
Solution
Given,
Principal (P) = $3950
Rate of Simple Interest (SI) = 8%
Time (t) = 5 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) = $3950 × 8% × 5
= $3950 ×8/100 × 5
= 3950 × 8 × 5/100
= 31600 × 5/100
= 158000/100
= $1580
Thus, Simple Interest = $1580
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 = $3950 + $1580
= $5530
Thus, Amount to be paid = $5530 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 = $3950
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 5 years
Thus, Amount (A)
= $3950 + ($3950 × 8% × 5)
= $3950 + ($3950 ×8/100 × 5)
= $3950 + (3950 × 8 × 5/100)
= $3950 + (31600 × 5/100)
= $3950 + (158000/100)
= $3950 + $1580 = $5530
Thus, Amount (A) to be paid = $5530 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 $3950, the simple interest in 1 year
= 8/100 × 3950
= 8 × 3950/100
= 31600/100 = $316
Thus, simple interest for 1 year = $316
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $316 × 5 = $1580
Thus, Simple Interest (SI) = $1580
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3950 + $1580
= $5530
Thus, Amount to be paid = $5530 Answer
Similar Questions
(1) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.
(2) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $10540 to clear the loan, then find the time period of the loan.
(3) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.
(4) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7072 to clear the loan, then find the time period of the loan.
(5) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.
(6) In how much time a principal of $3200 will amount to $3712 at a simple interest of 4% per annum?
(7) Calculate the amount due if David borrowed a sum of $3400 at 4% simple interest for 4 years.
(8) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6314 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.
(10) Mary had to pay $3507.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.