Question:
Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 8 years.
Correct Answer
$7280
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 5%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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) = $5200 × 5% × 8
= $5200 ×5/100 × 8
= 5200 × 5 × 8/100
= 26000 × 8/100
= 208000/100
= $2080
Thus, Simple Interest = $2080
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 = $5200 + $2080
= $7280
Thus, Amount to be paid = $7280 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 = $5200
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 8 years
Thus, Amount (A)
= $5200 + ($5200 × 5% × 8)
= $5200 + ($5200 ×5/100 × 8)
= $5200 + (5200 × 5 × 8/100)
= $5200 + (26000 × 8/100)
= $5200 + (208000/100)
= $5200 + $2080 = $7280
Thus, Amount (A) to be paid = $7280 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5200, the simple interest in 1 year
= 5/100 × 5200
= 5 × 5200/100
= 26000/100 = $260
Thus, simple interest for 1 year = $260
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $260 × 8 = $2080
Thus, Simple Interest (SI) = $2080
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $2080
= $7280
Thus, Amount to be paid = $7280 Answer
Similar Questions
(1) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 7% simple interest?
(2) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.
(3) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 5% simple interest?
(4) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 6% simple interest?
(5) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 5% simple interest?
(6) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.
(7) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.
(8) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10332 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Linda borrowed a sum of $3350 at 7% simple interest for 4 years.
(10) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.