I need help with questions have an idea how to do it but nee

I need help with questions have an idea how to do it but need to show work and not sure how to show my work ...

1. You decide to invest $15000 into a bank account that that is compounding its interest monthly. Assuming the bank is paying out an interest rate of the current prime rate - 1% (In the event that prime - 1% is less than 1%, use 1%), and the investment is for 5 years

a) How much money (total) do you have after the 5 years pass?

b) How much do you earn in interest over the 5 years?

2. You wish to have $500,000 saved up in 30 years. Assuming that you can get an interest rate of prime + 5% on your investment (compounded quarterly.)

            a) How much do you need to invest today to have $500,000 30 years in the future?

            b) How much of that total is interst

3. You borrow $50,000 at 5% interest (compounded daily).

            a) After 1 year passes, you pay off $25000 of the loan. How much do you still owe on the loan?

            b) After another year passes, you wish to pay off the loan. How much do you need to pay to pay it off

Solution

1. You decide to invest $15000 into a bank account that that is compounding its interest
monthly. Assuming the bank is paying out an interest rate of the current prime rate - 1%
(In the event that prime - 1% is less than 1%, use 1%), and the investment is for
5 years.

a) How much money (total) do you have after the 5 years pass?

A = P(1 + r/n)^nt

P = Principal amount (initial amount) = $15,000.00
r = annual rate of interest (as a decimal) = 0.01
t = number of years the account deposited or borrowed for = 5
n = number of times the interest is compounded per year = 12
A = amount of money accumulated after n years, including interest = $75,753.45 Answer

b) How much do you earn in interest over the 5 years?

Interest earned = $60,753.45 Answer

Question 2
(10 points)
2. You wish to have $500,000 saved up in 30 years. Assuming that you can get an interest rate of
prime + 5% on your investment (compounded quarterly).
NOTE: The prime rate of the previous problem (1%) is assumed.

a) How much do you need to invest today to have $500,000 30 years in the future? 27

Future value = $500,000.00
Number of compounding periods = 120
Interest rate for one compounding period = 0.015
Present value = $83,761.59 Answer

b) How much of that total is interest?

Interest earned = $416,238.41 Answer

Question 3
(10 points)
3. You borrow $50,000 at 5% interest (compounded daily).

a) After 1 year passes, you pay off $25000 of the loan. How much do you still owe on the loan?

P = Principal amount (initial amount) = $50,000.00
r = annual rate of interest (as a decimal) = 0.05
t = number of years the account deposited or borrowed for = 1
n = number of times the interest is compounded per year = 365
A = amount of money accumulated after n years, including interest = $52,563.37

Payment = $25,000.00

Remainder of debt = $27,563.37 Answer

b) After another year passes, you wish to pay off the loan. How much do you need to pay to pay it off?

P = Principal amount (initial amount) = $27,563.37
r = annual rate of interest (as a decimal) = 0.05
t = number of years the account deposited or borrowed for = 1
n = number of times the interest is compounded per year = 365
A = amount of money accumulated after n years, including interest = $28,976.48 Answer