Question:
What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 8% simple interest?
Correct Answer
$5390
Solution And Explanation
Solution
Given,
Principal (P) = $3850
Rate of Simple Interest (SI) = 8%
Time (t) = 5 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) = $3850 × 8% × 5
= $3850 ×8/100 × 5
= 3850 × 8 × 5/100
= 30800 × 5/100
= 154000/100
= $1540
Thus, Simple Interest = $1540
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 = $3850 + $1540
= $5390
Thus, Amount to be paid = $5390 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 = $3850
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 5 years
Thus, Amount (A)
= $3850 + ($3850 × 8% × 5)
= $3850 + ($3850 ×8/100 × 5)
= $3850 + (3850 × 8 × 5/100)
= $3850 + (30800 × 5/100)
= $3850 + (154000/100)
= $3850 + $1540 = $5390
Thus, Amount (A) to be paid = $5390 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 $3850, the simple interest in 1 year
= 8/100 × 3850
= 8 × 3850/100
= 30800/100 = $308
Thus, simple interest for 1 year = $308
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $308 × 5 = $1540
Thus, Simple Interest (SI) = $1540
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3850 + $1540
= $5390
Thus, Amount to be paid = $5390 Answer
Similar Questions
(1) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $13600 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 10% simple interest for 7 years.
(3) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.
(4) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9112 to clear the loan, then find the time period of the loan.
(5) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
(6) In how much time a principal of $3050 will amount to $3355 at a simple interest of 5% per annum?
(7) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.
(8) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Jennifer borrowed a sum of $3250 at 5% simple interest for 3 years.
(10) If Andrew paid $5760 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.