Question:
Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.
Correct Answer
$7735
Solution And Explanation
Solution
Given,
Principal (P) = $5950
Rate of Simple Interest (SI) = 3%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 10
= $5950 ×3/100 × 10
= 5950 × 3 × 10/100
= 17850 × 10/100
= 178500/100
= $1785
Thus, Simple Interest = $1785
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 + $1785
= $7735
Thus, Amount to be paid = $7735 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) = 3%
And, Time (t) = 10 years
Thus, Amount (A)
= $5950 + ($5950 × 3% × 10)
= $5950 + ($5950 ×3/100 × 10)
= $5950 + (5950 × 3 × 10/100)
= $5950 + (17850 × 10/100)
= $5950 + (178500/100)
= $5950 + $1785 = $7735
Thus, Amount (A) to be paid = $7735 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5950, the simple interest in 1 year
= 3/100 × 5950
= 3 × 5950/100
= 17850/100 = $178.5
Thus, simple interest for 1 year = $178.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $178.5 × 10 = $1785
Thus, Simple Interest (SI) = $1785
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $1785
= $7735
Thus, Amount to be paid = $7735 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.
(2) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6109 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 3 years.
(4) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $10430 to clear the loan, then find the time period of the loan.
(5) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(6) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.
(7) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8036 to clear the loan, then find the time period of the loan.
(8) How much loan did Jason borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8470 to clear it?
(9) What amount does John have to pay after 6 years if he takes a loan of $3200 at 7% simple interest?
(10) Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 8 years.