Question

Compute the future values of the following first assuming that payments are made on the last day of the period and then assuming payments are made on the first day of the period:

Payment	Years	Interest Rate	Future Value (Payment made on last day of period)	Future Value (Payment made on first day of period)
$    123	13	13%
4,555	8	8
74,484	5	10
167,332	9	1

Answer 1

Future Value of annuities:

Annuities are contracts sold by financial institutions like insurance companies or banks. When purchasing an annuity the investor invests the amount in lump sum or in an accumulation period. The future value of annuity is the amount the investor receives after investing in lump sum or in installment for a specific time period at a certain interest rate.

The equation for Future Value of an ordinary annuity is:

Here, is Future Value, is Payment amount, is the rate of interest, is number of compounding periods in the investment.

Ordinary annuity means the interest is paid at the end of the particular period.

The other type of annuity is Annuity Due, where the payments are made at the beginning of the period, the formula of the same is slightly different. We simply need to multiply the above formula by the factor.

The equation for Future Value of an annuity due is

Here, is Future Value, is Payment amount, is the rate of interest, is number of compounding periods in the investment.

Payment amount is

Number of years is

Rate if interest is

Calculate Ordinary Annuity:

Calculate Annuity Due:

Hence, the Future Value of Annuity at the end of the period is and at the beginning of the period is

Payment amount is

Number of years is

Rate if interest is

Calculate Ordinary Annuity:

Continuation of the above.

Calculate Annuity Due:

Hence, the Future Value of Annuity at the end of the period is and at the beginning of the period is

Payment amount is

Number of years is

Rate if interest is

Calculate Ordinary Annuity:

Calculate Annuity Due:

Hence, the Future Value of Annuity at the end of the period is and at the beginning of the period is

Payment amount is

Number of years is

Rate if interest is

Calculate Ordinary Annuity:

Calculate Annuity Due:

Hence, the Future Value of Annuity at the end of the period is and at the beginning of the period is

The following is the tabular representation of the answer:

The table above shows present values for payments made at the beginning of the period and on the last day of payment for different time periods as per the calculations explained previously.