When Martin was born, his father
set up a $5,000 college fund for him
with an annual compound interest
rate of 7.3%. What is the final
amount of this college fund, and
how much interest is gained if this
fund is invested for 18 years if
interest is compounded monthly?
Round the answers to two decimal
places as needed. (1 point)
The final amount of the college
fund is $, and the amount of
interest gained is $
To calculate the final amount of the college fund, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = final amount
P = principal (initial amount)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
Given:
P = $5,000
r = 7.3% = 0.073 (as a decimal)
n = 12 (compounded monthly)
t = 18
Plugging in the values:
A = 5000(1 + 0.073/12)^(12*18)
Calculating the expression within parentheses:
(1 + 0.073/12)^(12*18) = 1.604804
Now computing the final amount:
A = 5000 * 1.604804
A ≈ $8,024.02
Therefore, the final amount of the college fund is $8,024.02.
To calculate the amount of interest gained, we subtract the principal from the final amount:
Interest = A - P = $8,024.02 - $5,000 = $3,024.02
Therefore, the amount of interest gained is $3,024.02.
Angel wants to invest $7,000 for 3
years. He has two investing options.
• Option 1: Investing with a
15% simple interest rate.
• Option 2: Investing with a
12% compound interest rate,
with interest being
compounded quarterly.
Find the difference in interest
earnings to help Angel determine
which investing option will give
more financial returns.
To compare the interest earnings between Option 1 and Option 2, we need to calculate the interest earned for each option.
Option 1: Simple Interest
The formula for calculating simple interest is:
I = P * r * t
Where:
I = interest earned
P = principal
r = interest rate (as a decimal)
t = number of years
Given:
P = $7,000
r = 15% = 0.15 (as a decimal)
t = 3 years
Plugging in the values:
I = 7,000 * 0.15 * 3
I = $3,150
Option 1 earns $3,150 in interest.
Option 2: Compound Interest
The formula for calculating compound interest is:
A = P * (1 + r/n)^(nt) - P
Where:
A = amount after interest is compounded
P = principal
r = interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
Given:
P = $7,000
r = 12% = 0.12 (as a decimal)
n = 4 (compounded quarterly)
t = 3 years
Plugging in the values:
A = 7,000 * (1 + 0.12/4)^(4*3) - 7,000
Calculating the expression within parentheses:
(1 + 0.12/4)^(4*3) = 1.438976
Now computing the final amount:
A = 7,000 * 1.438976 - 7,000
A ≈ $9,372.83 - $7,000
A ≈ $2,372.83
Option 2 earns $2,372.83 in interest.
Therefore, the difference in interest earnings between the two options is:
Difference = Option 2 interest - Option 1 interest
= $2,372.83 - $3,150
= -$777.17
Based on these calculations, Option 1 earns more interest ($3,150) compared to Option 2 ($2,372.83). Therefore, Option 1 will give more financial returns.
A student with a 33,500 student
loan is offered two payment plans
to repay their debt.
• Plan 1: Monthly payment of
$361.91 over a period of 10
years, which corresponds to
a compound interest rate of
5.4% compounded monthly.
• Plan 2: Monthly payment of
$473.49 over a period of 7
years, which corresponds to
a compound interest rate of
5.0% compounded monthly.
Determine which plan offers the
student a lower cost of credit. Find
the lower credit cost. Round the
answer to two decimal places as
needed.
To determine which repayment plan offers a lower cost of credit, we need to compare the total amount paid for each plan.
Plan 1: Monthly payment of $361.91 over a period of 10 years, compounded monthly at 5.4%.
First, we need to calculate the total amount paid over the 10-year period. Since the monthly payment remains the same, we'll multiply it by the number of months in 10 years (12 months/year * 10 years):
Total amount paid = Monthly payment * Number of months
= $361.91 * (12 * 10)
= $361.91 * 120
= $43,429.20
Now, let's calculate the interest earned using the compound interest formula:
A = P * (1 + r/n)^(nt) - P
Where:
A = total amount after interest
P = principal (loan amount)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
Given:
P = $33,500
r = 5.4% = 0.054 (as a decimal)
n = 12 (compounded monthly)
t = 10 years
Plugging in the values:
A = 33,500 * (1 + 0.054/12)^(12*10) - 33,500
Calculating the expression within parentheses:
(1 + 0.054/12)^(12*10) = 1.715558
Now computing the final amount:
A = 33,500 * 1.715558 - 33,500
A ≈ $42,774.04 - $33,500
A ≈ $9,274.04
The total amount paid includes both the principal and the interest, so the cost of credit would be the total amount paid minus the principal:
Cost of credit for Plan 1 = Total amount paid - Principal
= $9,274.04 - $33,500
= -$24,225.96 (negative value indicates a loss)
Plan 1 has a negative cost of credit, meaning the student receives $24,225.96 instead of paying it back.
Plan 2: Monthly payment of $473.49 over a period of 7 years, compounded monthly at 5.0%.
Following the same process, we first calculate the total amount paid over the 7-year period:
Total amount paid = Monthly payment * Number of months
= $473.49 * (12 * 7)
= $473.49 * 84
= $39,815.16
Now, let's calculate the interest earned using the compound interest formula:
Given:
P = $33,500
r = 5.0% = 0.05 (as a decimal)
n = 12 (compounded monthly)
t = 7 years
A = 33,500 * (1 + 0.05/12)^(12*7) - 33,500
Calculating the expression within parentheses:
(1 + 0.05/12)^(12*7) = 1.421591
Now computing the final amount:
A = 33,500 * 1.421591 - 33,500
A ≈ $47,548.51 - $33,500
A ≈ $14,048.51
Cost of credit for Plan 2 = Total amount paid - Principal
= $14,048.51 - $33,500
= -$19,451.49 (negative value indicates a loss)
Plan 2 has a negative cost of credit, indicating a loss of $19,451.49.
Comparing the cost of credit between the two plans, we find that Plan 1 has a lower cost of credit ($24,225.96) compared to Plan 2 ($19,451.49).
Using an online calculator,
determine the total cost, fixed
monthly payment, and the total
interest paid when repaying a credit
card loan of $3,500 with a 21%
interest rate compounded monthly
over a 24-month term. Round the
answer to the nearest dollar.
(2 points)
To the nearest dollar, the total
cost of repaying the loan is $
____ The fixed monthly payment
Amount is $ _____ the total amount of interest paid is $ _______
Using an online compound interest calculator, we can determine the total cost, fixed monthly payment, and total interest paid for the credit card loan.
Given:
Principal (P) = $3,500
Interest Rate (r) = 21% per year (as a decimal)
Number of periods (t) = 24 months
Using the compound interest formula:
A = P * (1 + r/n)^(nt)
Where:
A = total amount after interest
n = number of times interest is compounded per year
Plugging in the values:
A = 3500 * (1 + 0.21/12)^(12*2)
Calculating the expression within parentheses:
(1 + 0.21/12)^(12*2) = 1.512043
Now computing the final amount:
A = 3500 * 1.512043
A ≈ $5,297.15
The nearest dollar total cost of repaying the loan is $5,297.
To find the fixed monthly payment, we divide the total cost by the number of months:
Fixed Monthly Payment = Total Cost / Number of Months
= $5,297 / 24
= $220.71
The nearest dollar fixed monthly payment amount is $221.
To calculate the total amount of interest paid, we subtract the principal from the total cost:
Total Interest Paid = Total Cost - Principal
= $5,297 - $3,500
= $1,797
The nearest dollar total amount of interest paid is $1,797.
Kris is looking to purchase a $599
laptop. They have $350 in cash, a
$100 gift card, and a credit card
with an $800 limit. Identify the
payment method that can cover the
cost of the new laptop.
Method 1: cash
Method 2: gift card
Method 3: credit card (1 point)
The payment method that can
cover the cost of the new laptop
is payment Method
The payment method that can cover the cost of the new laptop is payment Method 3: credit card.
Kris has $350 in cash, which is not enough to cover the full cost of the laptop. The $100 gift card can help reduce the remaining balance, but it is still not sufficient to cover the full amount.
However, Kris has a credit card with an $800 limit. This means they have enough credit available to make the purchase. They can use their credit card to pay for the laptop and cover the cost.
Therefore, payment Method 3, using the credit card, is the payment method that can cover the cost of the new laptop.
Dallas needs a new refrigerator that
costs $799. Which of the following
payment methods should Dallas
use to pay for the refrigerator?
Dallas wants to make sure there are
sufficient funds to cover the
purchases and minimize the
interest, if any, that will be needed
to pay for the purchases.
Method 1: He should use the debit
card with a $600 balance.
Method 2: He should use the credit
card with a $1,000 credit limit and a
potential 5% interest on the
purchases if the amount is not paid
in full by the statement's due date.
Method 3: He should use a $799
payday loan with 7% interest.