Savings annuity calculator with graph help

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Calculate The savings annuity calculates the future value of a stream of equal payments made at regular intervals over a specified period of time at a given interest rate.
 FV = PMT * ((1 + R / N)N * T - 1) or FV = PMT * ((1 + r)N * T - 1) R / N r

FV = N * T * PMT + I = A + I
r = R / N

where:
FV = Future value
I = Interest amount
A = Total payment amount
R = Nominal interest rate per year (as a decimal, not in percentage)
r = Interest rate per period (as a decimal, not in percentage)
T = Time period in years
N = Number of compounding periods in one year
PMT = Periodic payment amount, paid at the end of each payment period

Other variations of the savings annuity equation are used to calculate:
• The future value (FV)

 FV = PMT * ((1 + R/N)N * T - 1) R / N

• The periodic payment amount (PMT)  PMT = FV * (R/N) and FV = N * T * PMT + I (1 + (R / N))N * T -1

Note:
A sinking fund is when we know the future value of the annuity and wish to calculate the periodic payment amount.

• The nominal annual interest rate (R) (as a decimal, not in percentage)  FV = (1 + (R / N))N * T - 1 PMT R / N
Note:
Keep substituting different values for R until we get successively closer to the desired value of FV / PMT.

• The time period (T) in years

 T = log((R / N) * ((FV / PMT) + (N / R))) and FV = N * T * PMT + I N * log(1 + (R / N))
• The compounding periods (N) in one year

 N = log(((FV * r) / PMT) + 1) and FV = N * T * PMT + I T * log(1 + r)
Note:
r = interest rate per period

For example, if you borrow \$1000 for 2 years at 12% interest compounded quarterly, you must divide the annual interest rate by 4 to obtain the interest rate per period
(r = R / N = 12 / 4 = 3%).

• The effective interest rate (Re) (as a decimal, not in percentage)

Re = (1 + (R / N))N   - 1          or          Re = (1 + r)N   - 1

Note:
The effective interest rate is the equivalent rate of compound interest earned over a period of one year for a nominal interest rate per year which is compounded twice or more over the year.