Question:
Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.
Correct Answer
$7684
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 4%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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) = $5650 × 4% × 9
= $5650 ×4/100 × 9
= 5650 × 4 × 9/100
= 22600 × 9/100
= 203400/100
= $2034
Thus, Simple Interest = $2034
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 = $5650 + $2034
= $7684
Thus, Amount to be paid = $7684 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 = $5650
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 9 years
Thus, Amount (A)
= $5650 + ($5650 × 4% × 9)
= $5650 + ($5650 ×4/100 × 9)
= $5650 + (5650 × 4 × 9/100)
= $5650 + (22600 × 9/100)
= $5650 + (203400/100)
= $5650 + $2034 = $7684
Thus, Amount (A) to be paid = $7684 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5650, the simple interest in 1 year
= 4/100 × 5650
= 4 × 5650/100
= 22600/100 = $226
Thus, simple interest for 1 year = $226
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $226 × 9 = $2034
Thus, Simple Interest (SI) = $2034
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $2034
= $7684
Thus, Amount to be paid = $7684 Answer
Similar Questions
(1) How much loan did Betty borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7812.5 to clear it?
(2) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 7 years.
(3) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 8% simple interest?
(4) Calculate the amount due if Linda borrowed a sum of $3350 at 10% simple interest for 3 years.
(5) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.
(6) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.
(7) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7421 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 8 years.
(9) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.
(10) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.