Question:
Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.
Correct Answer
$8755
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 7%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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) = $5150 × 7% × 10
= $5150 ×7/100 × 10
= 5150 × 7 × 10/100
= 36050 × 10/100
= 360500/100
= $3605
Thus, Simple Interest = $3605
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 = $5150 + $3605
= $8755
Thus, Amount to be paid = $8755 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 = $5150
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 10 years
Thus, Amount (A)
= $5150 + ($5150 × 7% × 10)
= $5150 + ($5150 ×7/100 × 10)
= $5150 + (5150 × 7 × 10/100)
= $5150 + (36050 × 10/100)
= $5150 + (360500/100)
= $5150 + $3605 = $8755
Thus, Amount (A) to be paid = $8755 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5150, the simple interest in 1 year
= 7/100 × 5150
= 7 × 5150/100
= 36050/100 = $360.5
Thus, simple interest for 1 year = $360.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $360.5 × 10 = $3605
Thus, Simple Interest (SI) = $3605
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $3605
= $8755
Thus, Amount to be paid = $8755 Answer
Similar Questions
(1) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 7% simple interest?
(2) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 8% simple interest?
(3) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $10064 to clear the loan, then find the time period of the loan.
(4) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.
(5) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 6% simple interest?
(6) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 9% simple interest.
(7) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 10% simple interest?
(9) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $12060 to clear the loan, then find the time period of the loan.
(10) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 9% simple interest?