Question:
Find the amount to be paid if Susan borrowed a sum of $5650 at 4% simple interest for 8 years.
Correct Answer
$7458
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 4%
Time (t) = 8 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% × 8
= $5650 ×4/100 × 8
= 5650 × 4 × 8/100
= 22600 × 8/100
= 180800/100
= $1808
Thus, Simple Interest = $1808
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 + $1808
= $7458
Thus, Amount to be paid = $7458 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) = 8 years
Thus, Amount (A)
= $5650 + ($5650 × 4% × 8)
= $5650 + ($5650 ×4/100 × 8)
= $5650 + (5650 × 4 × 8/100)
= $5650 + (22600 × 8/100)
= $5650 + (180800/100)
= $5650 + $1808 = $7458
Thus, Amount (A) to be paid = $7458 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 8 years
= Simple interest for 1 year × 8
= $226 × 8 = $1808
Thus, Simple Interest (SI) = $1808
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $1808
= $7458
Thus, Amount to be paid = $7458 Answer
Similar Questions
(1) How much loan did Mark borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7360 to clear it?
(2) Calculate the amount due if James borrowed a sum of $3000 at 10% simple interest for 4 years.
(3) If Michael paid $3960 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(4) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 5% simple interest?
(5) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.
(6) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.
(7) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8195 to clear the loan, then find the time period of the loan.
(8) What amount does John have to pay after 5 years if he takes a loan of $3200 at 8% simple interest?
(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 4 years.
(10) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7708 to clear the loan, then find the time period of the loan.