Question:
Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.
Correct Answer
$8925
Solution And Explanation
Solution
Given,
Principal (P) = $5950
Rate of Simple Interest (SI) = 5%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 10
= $5950 ×5/100 × 10
= 5950 × 5 × 10/100
= 29750 × 10/100
= 297500/100
= $2975
Thus, Simple Interest = $2975
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 + $2975
= $8925
Thus, Amount to be paid = $8925 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) = 5%
And, Time (t) = 10 years
Thus, Amount (A)
= $5950 + ($5950 × 5% × 10)
= $5950 + ($5950 ×5/100 × 10)
= $5950 + (5950 × 5 × 10/100)
= $5950 + (29750 × 10/100)
= $5950 + (297500/100)
= $5950 + $2975 = $8925
Thus, Amount (A) to be paid = $8925 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5950, the simple interest in 1 year
= 5/100 × 5950
= 5 × 5950/100
= 29750/100 = $297.5
Thus, simple interest for 1 year = $297.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $297.5 × 10 = $2975
Thus, Simple Interest (SI) = $2975
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $2975
= $8925
Thus, Amount to be paid = $8925 Answer
Similar Questions
(1) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.
(2) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 4 years.
(4) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 4% simple interest?
(5) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.
(6) What amount does William have to pay after 5 years if he takes a loan of $3500 at 5% simple interest?
(7) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.
(8) Sandra had to pay $4717 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 3 years.
(10) If Joseph paid $4144 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.