math,help

posted by .

what formula do i use for the following problem:

which of the following investments is larger after 19years?
a) $7500 is deposited annually and earns 4.5% interest compounded annually.
b)$600 is deposited monthly and earns 4.5% interest compounded monthly.

Does he deposit the money at the beginning of the month/year (future annutity due) or the end of the month/year (ordinary annuity)?

(Broken Link Removed)

The answer depends on when the annuity is deposited

it doesn't say , so what do you think of the formula i should use.

What will R dollars deposited in a bank account at the end of each of n periods, and earning interest at I%, compounded n times per year, amount to in N years?
This is called an ordinary annuity, differeing from an annuity due. An ordinary annuity consists of a definite number of deposits made at the ENDS of equal intervals of time. An annuity due consists of a definite number of deposits made at the BEGINNING of equal intervals of time.
For an ordinary annuity over n payment periods, n deposits are made at the end of each period but interest is paid only on (n - 1) of the payments, the last deposit drawing no interest, obviously. In the annuity due, over the same n periods, interest accrues on all n payments and there is no payment made at the end of the nth period.
The formula for determining the accumulation of a series of periodic deposits, made at the end of each period, over a given time span is

S(n) = R[(1 + i)^n - 1]/i

where S(n) = the accumulation over the period of n inter, P = the periodic deposit, n = the number of interest paying periods, and i = the annual interest % divided by 100 divided by the number of interest paying periods per year. This is known as an ordinary annuity.
When an annuity is cumputed on the basis of the payments being made at the beginning of each period, an annuity due, the total accumulation is based on one more period minus the last payment. Thus, the total accumulation becomes

S(n+1) = R[(1 + i)^(n+1) - 1]/i - R = R[{(1 + i)^(n + 1) - 1}/i - 1]

Simple example: $200 deposited annually for 5 years at 12% annual interest compounded annually. Therefore, R = 200, n = 5, and i = .12.

Ordinary Annuity
..................................Deposit.......Interest.......Balance
Beginning of month 1........0................0.................0
End of month..........1.....200...............0...............200
Beg. of month.........2.......0.................0...............200
End of month..........2.....200..............24...............424
Beg. of month.........3.......0.................0................424
End of month..........3.....200............50.88..........674.88
Beg. of month.........4.......0.................0.............674.88
End of month..........4.....200............80.98..........955.86
Beg. of month.........5.......0.................0.............955.86
End of month..........5.....200...........114.70........1270.56

S = R[(1 + i)^n - 1]/i = 200[(1.12)^5 - 1]/.12 = $1270.56

Annuity Due
..................................Deposit.......Interest.......Balance
Beginning of month 1......200..............0................200
End of month..........1.......0...............24................224
Beg. of month.........2.....200..............0..................424
End of month..........2.......0.............50.88...........474.88
Beg. of month.........3.....200..............0...............674.88
End of month..........3.......0.............80.98...........755.86
Beg. of month.........4.....200..............0..............955.86
End of month..........4.......0...........114.70..........1070.56
Beg. of month.........5.....200..............0..............1270.56
End of month..........5.......0...........152.47..........1423.03

S = [R[(1 + i)^(n +1) - 1]/i - R] = 200[(1.12)^6 - 1]/.12 - 200 = $1,423.03


what is the name of the formula you are using?

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math

    Please check my work, thank you If $7,800 is deposited into an account paying 6% interest compounded annually (at the end of each year), how much money is in the account after 2 years?
  2. Business Algebra

    Invest $23,000 in a savings account at 4.25% interest compounded quarterly. Invest into an ordinary annuity where $5,000 is deposited each year into an account that earns 6.6% interest compounded annually.
  3. Business Algebra

    I need to know the formula for these questions and just how to do them. If you could help please. As a financial planner a client comes to you for investment advice. After meeting with him and understanding his needs, you offer him …
  4. Business Algebra

    Part I: As a financial planner a client comes to you for investment advice. After meeting with him and understanding his needs, you offer him the following two investment options: Option 1 (refer to section on Mathematics of Finance …
  5. Simple & Compounding Interest

    I am SO STUCK on this problem... PLEASE HELP ASAP!!! Suppose Kevin and Jill both deposit $4000 into their personal accounts. If Kevin’s account earns 5% simple interest annually and Jill’s earns 5% interest compounded annually, …
  6. Algebra

    Show how you substitute the values into the formula, then use your calculator. *Use A = P(1+r/n)nt to find the amount of money in an account after t years, compounded n times per year. *Use I = Prt to find the amount of simple interest …
  7. Math

    Deana invests some money that earns interest compounded annually. At the end of the first year, she earns $400 in interest. At the end of the second year, she earns $432 in interest. a) what interest rate, compounded annually, is deana …
  8. Lat math question for some days. Can y'all help?

    Huan deposited $850 into a college savings account earning 4.8% interest compounded annually. He also deposited $850 into a second account earning 4.8% simple interest. He made no additional deposits. After 10 years, which account …
  9. Computer Science

    i Need help, using loops, visual studio 2013. write a program using loops that will calculate the following, how much would $24 deposited in a bank in 1626, have been worth at the end of this year if it had received an interest rate …
  10. Math

    Brody deposited $500 into an account that earns 4.2% interest compounded annually. He makes no additional deposits and no withdrawals. Approximately how much interest will the account have earned after 7 years?

More Similar Questions