Question:
Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 8 years.
Correct Answer
$8362
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 6%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 8
= $5650 ×6/100 × 8
= 5650 × 6 × 8/100
= 33900 × 8/100
= 271200/100
= $2712
Thus, Simple Interest = $2712
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 + $2712
= $8362
Thus, Amount to be paid = $8362 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) = 6%
And, Time (t) = 8 years
Thus, Amount (A)
= $5650 + ($5650 × 6% × 8)
= $5650 + ($5650 ×6/100 × 8)
= $5650 + (5650 × 6 × 8/100)
= $5650 + (33900 × 8/100)
= $5650 + (271200/100)
= $5650 + $2712 = $8362
Thus, Amount (A) to be paid = $8362 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5650, the simple interest in 1 year
= 6/100 × 5650
= 6 × 5650/100
= 33900/100 = $339
Thus, simple interest for 1 year = $339
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $339 × 8 = $2712
Thus, Simple Interest (SI) = $2712
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $2712
= $8362
Thus, Amount to be paid = $8362 Answer
Similar Questions
(1) If Barbara borrowed $3550 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(2) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 3 years.
(3) How much loan did Andrew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7820 to clear it?
(4) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 10% simple interest?
(5) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.
(6) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 4% simple interest?
(7) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
(8) If William paid $3920 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 7% simple interest?
(10) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.