After a protracted legal case, Joe won a settlement that will pay him $11,000 each year for the next ten years. If the market interest rates are currently 5%, exactly how much should the court invest today, assuming end of year payments, so there will be nothing left in the account after the final payment is made?

Mary just deposited $33,000 in an account paying 7% interest. She plans to leave the money in this account for eight years. How much will she have in the account at the end of the seventh year?

Mary and Joe would like to save up $10,000 by the end of three years from now to buy new furniture for their home. They currently have $1500 in a savings account set aside for the furniture. They would like to make equal year end deposits to this savings account to pay for the furniture when they purchase it three years from now. Assuming that this account pays 6% interest, how much should the year end payments be?

An excel spreadsheet is very helpful for these kinds of calculations.


The balance after 1 year is B1=B0*(1+r)-P, Where B0 is the initial balance and P is the payment=11000, r is the rate of interest = .05

After 2 years its B2 = B1*(1+r)-P = (B0*(1+r)-P)*(1+r) - P
= B0*(1+r)^2 - P(1 + (1+r))

so, by extension,
B10 = B0*(1+r)^10 - P*sum[(1+r)^(n-1)]
one equation, one unknown, solve for B0

part 1

PV=FV*PVif (N=10yrs. i=5%)
PV=1,000 X 7.722
PV= $84,942.00 ANSWER

PART 3
FV=PV X FVif 7% of 8 years
FV=33,000 X 1.718
FV= 56,694.00

How much would you repay the bank if you borrowed $7,900 at 4.3% annual interest for 6 years

To determine the amount that should be invested today in order to pay Joe $11,000 each year for the next ten years, we need to use the concept of present value. The present value formula is given by:

PV = PMT * (1 - (1 + r)^(-n)) / r

where PV is the present value, PMT is the annual payment, r is the interest rate, and n is the number of years.

In this case, PMT is $11,000, r is 5%, and n is 10. We can substitute these values into the formula to find the present value:

PV = 11,000 * (1 - (1 + 0.05)^(-10)) / 0.05
PV = 11,000 * (1 - 0.613913) / 0.05
PV = 11,000 * 0.386087 / 0.05
PV = 84,494.52

Therefore, the court should invest approximately $84,494.52 today in order to pay Joe $11,000 each year for the next ten years.

To calculate how much Mary will have in her account at the end of the seventh year, we can use the compound interest formula:

A = P * (1 + r)^n

where A is the amount at the end, P is the initial deposit, r is the interest rate, and n is the number of years.

In this case, P is $33,000, r is 7%, and n is 7. We can substitute these values into the formula to find the amount at the end of the seventh year:

A = 33,000 * (1 + 0.07)^7
A = 33,000 * (1.07)^7
A = 33,000 * 1.718708
A = 56,676.24

Therefore, Mary will have approximately $56,676.24 in her account at the end of the seventh year.

To calculate the year-end payments that Mary and Joe should make in order to save up $10,000 over three years, we can use the future value of an annuity formula:

FV = PMT * ((1 + r)^n - 1) / r

where FV is the future value, PMT is the annual payment, r is the interest rate, and n is the number of years.

In this case, FV is $10,000, PMT is the unknown, r is 6%, and n is 3. We can rearrange the formula to solve for PMT:

PMT = FV * r / ((1 + r)^n - 1)
PMT = 10,000 * 0.06 / ((1 + 0.06)^3 - 1)
PMT = 10,000 * 0.06 / (1.191016 - 1)
PMT = 10,000 * 0.06 / 0.191016
PMT = 3129.56

Therefore, Mary and Joe should make year-end payments of approximately $3,129.56 in order to save up $10,000 over three years.