Question:
Find the amount to be paid if Jennifer borrowed a sum of $5250 at 6% simple interest for 8 years.
Correct Answer
$7770
Solution And Explanation
Solution
Given,
Principal (P) = $5250
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) = $5250 × 6% × 8
= $5250 ×6/100 × 8
= 5250 × 6 × 8/100
= 31500 × 8/100
= 252000/100
= $2520
Thus, Simple Interest = $2520
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 = $5250 + $2520
= $7770
Thus, Amount to be paid = $7770 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 = $5250
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 8 years
Thus, Amount (A)
= $5250 + ($5250 × 6% × 8)
= $5250 + ($5250 ×6/100 × 8)
= $5250 + (5250 × 6 × 8/100)
= $5250 + (31500 × 8/100)
= $5250 + (252000/100)
= $5250 + $2520 = $7770
Thus, Amount (A) to be paid = $7770 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 $5250, the simple interest in 1 year
= 6/100 × 5250
= 6 × 5250/100
= 31500/100 = $315
Thus, simple interest for 1 year = $315
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $315 × 8 = $2520
Thus, Simple Interest (SI) = $2520
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5250 + $2520
= $7770
Thus, Amount to be paid = $7770 Answer
Similar Questions
(1) What amount does David have to pay after 6 years if he takes a loan of $3400 at 7% simple interest?
(2) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $6854 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 8 years.
(4) How much loan did Melissa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8820 to clear it?
(5) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.
(6) In how much time a principal of $3200 will amount to $3840 at a simple interest of 5% per annum?
(7) In how much time a principal of $3000 will amount to $3270 at a simple interest of 3% per annum?
(8) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 8 years.
(9) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 4 years.