Question

What is the present value of $4,320 to be received at the beginning of each of 28 periods, discounted at 5% compound interest? (Round factor values to 5 decimal places, e.g. 1.25124 and final answer to 0 decimal places, e.g. 458,581.)

What is the future value of 16 deposits of $3,970 each made at the beginning of each period and compounded at 10%? (Future value as of the end of the 16th period.) (Round factor values to 5 decimal places, e.g. 1.25124 and final answer to 0 decimal places, e.g. 458,581.)

What is the present value of 6 receipts of $3,010 each received at the beginning of each period, discounted at 9% compounded interest? (Round factor values to 5 decimal places, e.g. 1.25124 and final answer to 0 decimal places, e.g. 458,581.)

Answer 1

Present value of annuity is the present worth of cash flows that is to be received in the future, if future Present Value of an annuity due is used to determine the present value of a stream of equal payments where the payment occurs at the beginning of each period.

If,

Periodic payment (P) = 4320

Interest rate (i) = 0.05

Time period (n) = 28

Then PV of annuity due = P * (1 + i) [1 - {(1+ i)^-n}/i]

Lets put all the values in the formula to find PV of annuity due,

PV of annuity due = 4320* (1 + 0.05) [{1- (1 + 0.05)^- 28}/ 0.05]

                                      = 4320* (1.05) [{1- (1.05)^- 28}/ 0.05]

                                      = 4536[{1- 0.2550936371}/ 0.05]

                                      = 4536[0.7449063629/ 0.05]

                                      = 4536* 14.89813

                                      = 67577.91768

So PV of annuity due is $67577.92

--------------------------------------------------------------------------------------------------------------------------

The future value of annuity due formula is used to calculate the ending value of a series of payments or cash flows where the first payment is received immediately. The first cash flow received immediately is what distinguishes an annuity due from an ordinary annuity.

FV of annuity due = (1 + i) * P [{(1 + i) ^n -1}/i]

Where,

Periodic deposit (P) = $3970

Interest rate = 10%

Time (n) = 16

Let's put all the values in the formula to solve for FV of annuity due

FV of annuity due = (1 + 0.1) * 3970 [{(1 + 0.1) ^16- 1}/ 0.1]

                                     = (1.1) * 3970 [{(1.1) ^16- 1}/ 0.1]

                                     = 4367 *[4.59497298635722- 1/ 0.1]

                                     = 4367 *[3.59497298635722/ 0.1]

                                     = 4367 * 35.9497298635722

                                     = 156992.47

So FV of annuity due is $156992.47

--------------------------------------------------------------------------------------------------------------------------

If,

Periodic payment (P) = 3010

Interest rate (i) = 0.09

Time period (n) = 6

Then PV of annuity due = P * (1 + i) [1 - {(1+ i)^-n}/i]

Lets put all the values in the formula to find PV of annuity due,

PV of annuity due = 3010* (1 + 0.09) [{1- (1 + 0.09)^- 6}/ 0.09]

                                      = 3010* (1.09) [{1- (1.09)^- 6}/ 0.09]

                                      = 3280.9[{1- 0.5962673269}/ 0.09]

                                      = 3280.9[0.4037326731/ 0.09]

                                      = 3280.9* 4.48592

                                      = 14717.85493

So PV of annuity due is $14717.85

--------------------------------------------------------------------------------------------------------------------------

Feel free to comment if you need further assistance J

Pls rate this answer if you found it useful.