Question:
Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.
Correct Answer
$9990
Solution And Explanation
Solution
Given,
Principal (P) = $5550
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) = $5550 × 8% × 10
= $5550 ×8/100 × 10
= 5550 × 8 × 10/100
= 44400 × 10/100
= 444000/100
= $4440
Thus, Simple Interest = $4440
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 = $5550 + $4440
= $9990
Thus, Amount to be paid = $9990 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 = $5550
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 10 years
Thus, Amount (A)
= $5550 + ($5550 × 8% × 10)
= $5550 + ($5550 ×8/100 × 10)
= $5550 + (5550 × 8 × 10/100)
= $5550 + (44400 × 10/100)
= $5550 + (444000/100)
= $5550 + $4440 = $9990
Thus, Amount (A) to be paid = $9990 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 $5550, the simple interest in 1 year
= 8/100 × 5550
= 8 × 5550/100
= 44400/100 = $444
Thus, simple interest for 1 year = $444
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $444 × 10 = $4440
Thus, Simple Interest (SI) = $4440
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5550 + $4440
= $9990
Thus, Amount to be paid = $9990 Answer
Similar Questions
(1) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 6% simple interest?
(2) Nancy had to pay $4772.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 4% simple interest?
(4) Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 7 years.
(5) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 8 years.
(6) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $5984 to clear the loan, then find the time period of the loan.
(7) How much loan did Robert borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5610 to clear it?
(8) What amount does James have to pay after 5 years if he takes a loan of $3000 at 7% simple interest?
(9) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 10% simple interest?
(10) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $10106 to clear the loan, then find the time period of the loan.