Question:
Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.
Correct Answer
$9090
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 8%
Time (t) = 10 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) = $5050 × 8% × 10
= $5050 ×8/100 × 10
= 5050 × 8 × 10/100
= 40400 × 10/100
= 404000/100
= $4040
Thus, Simple Interest = $4040
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 = $5050 + $4040
= $9090
Thus, Amount to be paid = $9090 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 = $5050
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 10 years
Thus, Amount (A)
= $5050 + ($5050 × 8% × 10)
= $5050 + ($5050 ×8/100 × 10)
= $5050 + (5050 × 8 × 10/100)
= $5050 + (40400 × 10/100)
= $5050 + (404000/100)
= $5050 + $4040 = $9090
Thus, Amount (A) to be paid = $9090 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 $5050, the simple interest in 1 year
= 8/100 × 5050
= 8 × 5050/100
= 40400/100 = $404
Thus, simple interest for 1 year = $404
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $404 × 10 = $4040
Thus, Simple Interest (SI) = $4040
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $4040
= $9090
Thus, Amount to be paid = $9090 Answer
Similar Questions
(1) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 4 years.
(2) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 7 years.
(4) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8520 to clear the loan, then find the time period of the loan.
(5) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13800 to clear the loan, then find the time period of the loan.
(6) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6390 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.
(8) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8740 to clear the loan, then find the time period of the loan.
(9) What amount does David have to pay after 5 years if he takes a loan of $3400 at 4% simple interest?
(10) If Jessica borrowed $3750 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.