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 the following two investment options:
Option 1 (refer to section on Mathematics of Finance in your text.): Invest $23,000 in a savings account at 4.25% interest compounded quarterly.
Option 2 (refer to section on Mathematics of Finance in your text): Invest into an ordinary annuity where $5,000 is deposited each year into an account that earns 6.6% interest compounded annually.
Are you supposed to compare the relative merits of these options? The value of an annuity depends upon the actuarial probability of different expected life spans (expected number of payouts), and upon when the payouts begin. At death, the value of an annuity is zero.
Expected life span depends upon the age, sex, smoking history, obesity and general health (pre-existing conditions) of the individual.
Anyway, you have not asked a question yet and we do not have access to your text.
Yes. I just don't know how to do them. I have tried and would just like some help please. Thanks
Now, I have the formula's I am to use and just can't figure out if it is correct.
Quarterly = P (1 + r/4)4 = (quarterly compounding)
$23,000 (1+0.0425/4) 4 = $28,994.38
Annually = P × (1 + r) = (annual compounding)
$5,000 x (1+0.066) = $5,330
Is this correct?
Then I have to use a worksheet and I have no clue how to do this one.
SPREADSHEET:
Set up the formula for compound interest for Option 1 and the formula for Future Value of an Annuity for Option 2 in an Excel spreadsheet to calculate the amount earned at the end of 5 years. Be sure to label all variables in your spreadsheet. Be sure to upload your spreadsheet for formula verification.
You seem to be on the right track. We appreciate the feedback.
This is not my field of expertise but one of our other teachers might be able to help.
Taking option 1 from first principles
At time 0 there is $23000
after quarter 1 there is $23000x(1.0425)
after quarter 2 there is $23000x(1.0425)x1.0425
after quarter n there is $23000x(1.0425)^n
With option 2
at time zero there is $5000
after year 1 there is $5000x1.066+$5000
after year 2 there is $5000x1.066x1.066+$5000+45000
after year n there is $5000x(1.066)^n+$5000x(n)
I am not quite sure what you plan to do with these. Initially option 2 is the better, but after about 25 years Option is better. You need to plot these to decide, or solve mathematically.
In the question Option 1 does not state annual interest which your formula implies.
And from my post
after year 2 there is $5000x1.066x1.066+$5000+45000
should be
after year 2 there is $5000x1.066x1.066+$5000+$5000
I got it now. I understand. Thanks so much for your help. Perfect!!!
To solve these two investment options, you will need to use the formulas in the Mathematics of Finance section of your text. Let's break down each option and the corresponding formulas.
Option 1:
Invest $23,000 in a savings account at 4.25% interest compounded quarterly.
The formula you need to use for compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (expressed as a decimal)
n = the number of times interest is compounded per year
t = the number of years the money is invested for
In this case, you are given:
P = $23,000
r = 4.25% (or 0.0425 as a decimal)
n = 4 (quarterly compounding)
t = unknown
You need to solve for the unknown variable t, which represents the number of years the money is invested for. Rearrange the formula to solve for t:
t = (log(A/P))/(n*log(1+r/n))
Substitute the known values into the formula and solve for t.
Option 2:
Invest into an ordinary annuity where $5,000 is deposited each year into an account that earns 6.6% interest compounded annually.
The formula you need to use for the future value of an annuity is:
FV = P * ((1 + r)^n - 1) / r
Where:
FV = the future value of the annuity (the total amount of money accumulated)
P = the annual payment (or deposit) amount
r = the interest rate per compounding period (expressed as a decimal)
n = the number of compounding periods (in this case, it is equal to the number of years)
In this case, you are given:
P = $5,000
r = 6.6% (or 0.066 as a decimal)
n = unknown
You need to solve for the unknown variable n, which represents the number of years the annuity is invested for. Rearrange the formula to solve for n:
n = (log(1 + (FV*r)/P))/log(1 + r)
Substitute the known values into the formula and solve for n.
By using these formulas and plugging in the given values, you can calculate the future values of both investment options and compare the results, allowing you to provide the client with investment advice based on their needs.