Question:
Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 2% simple interest.
Correct Answer
$6600
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 2%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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) = $5500 × 2% × 10
= $5500 ×2/100 × 10
= 5500 × 2 × 10/100
= 11000 × 10/100
= 110000/100
= $1100
Thus, Simple Interest = $1100
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 = $5500 + $1100
= $6600
Thus, Amount to be paid = $6600 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 = $5500
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 10 years
Thus, Amount (A)
= $5500 + ($5500 × 2% × 10)
= $5500 + ($5500 ×2/100 × 10)
= $5500 + (5500 × 2 × 10/100)
= $5500 + (11000 × 10/100)
= $5500 + (110000/100)
= $5500 + $1100 = $6600
Thus, Amount (A) to be paid = $6600 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5500, the simple interest in 1 year
= 2/100 × 5500
= 2 × 5500/100
= 11000/100 = $110
Thus, simple interest for 1 year = $110
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $110 × 10 = $1100
Thus, Simple Interest (SI) = $1100
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $1100
= $6600
Thus, Amount to be paid = $6600 Answer
Similar Questions
(1) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.
(2) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.
(3) How much loan did William borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6325 to clear it?
(4) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 4% simple interest?
(5) If Elizabeth paid $4140 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) Andrew had to pay $5232 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 5% simple interest?
(8) Karen had to pay $4542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) What amount will be due after 2 years if David borrowed a sum of $3200 at a 6% simple interest?
(10) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 5% simple interest?