Question:
Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 8 years.
Correct Answer
$9282
Solution And Explanation
Solution
Given,
Principal (P) = $5950
Rate of Simple Interest (SI) = 7%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 8
= $5950 ×7/100 × 8
= 5950 × 7 × 8/100
= 41650 × 8/100
= 333200/100
= $3332
Thus, Simple Interest = $3332
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 + $3332
= $9282
Thus, Amount to be paid = $9282 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) = 7%
And, Time (t) = 8 years
Thus, Amount (A)
= $5950 + ($5950 × 7% × 8)
= $5950 + ($5950 ×7/100 × 8)
= $5950 + (5950 × 7 × 8/100)
= $5950 + (41650 × 8/100)
= $5950 + (333200/100)
= $5950 + $3332 = $9282
Thus, Amount (A) to be paid = $9282 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5950, the simple interest in 1 year
= 7/100 × 5950
= 7 × 5950/100
= 41650/100 = $416.5
Thus, simple interest for 1 year = $416.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $416.5 × 8 = $3332
Thus, Simple Interest (SI) = $3332
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $3332
= $9282
Thus, Amount to be paid = $9282 Answer
Similar Questions
(1) Find the amount to be paid if John borrowed a sum of $5200 at 2% simple interest for 7 years.
(2) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.
(3) Richard had to pay $4140 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 7% simple interest?
(5) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.
(6) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.
(7) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 3% simple interest.
(9) In how much time a principal of $3050 will amount to $3233 at a simple interest of 3% per annum?
(10) Donna had to pay $5577.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.