Question:
Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.
Correct Answer
$7556.5
Solution And Explanation
Solution
Given,
Principal (P) = $5950
Rate of Simple Interest (SI) = 3%
Time (t) = 9 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% × 9
= $5950 ×3/100 × 9
= 5950 × 3 × 9/100
= 17850 × 9/100
= 160650/100
= $1606.5
Thus, Simple Interest = $1606.5
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 + $1606.5
= $7556.5
Thus, Amount to be paid = $7556.5 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) = 9 years
Thus, Amount (A)
= $5950 + ($5950 × 3% × 9)
= $5950 + ($5950 ×3/100 × 9)
= $5950 + (5950 × 3 × 9/100)
= $5950 + (17850 × 9/100)
= $5950 + (160650/100)
= $5950 + $1606.5 = $7556.5
Thus, Amount (A) to be paid = $7556.5 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 9 years
= Simple interest for 1 year × 9
= $178.5 × 9 = $1606.5
Thus, Simple Interest (SI) = $1606.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $1606.5
= $7556.5
Thus, Amount to be paid = $7556.5 Answer
Similar Questions
(1) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.
(2) How much loan did Christopher borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6900 to clear it?
(3) Calculate the amount due if Christopher borrowed a sum of $4000 at 5% simple interest for 3 years.
(4) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11880 to clear the loan, then find the time period of the loan.
(5) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.
(6) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Charles borrowed a sum of $3900 at 10% simple interest for 4 years.
(8) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 5% simple interest?
(9) Emily had to pay $5462.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 5% simple interest.