Question

For each of the following situations involving annuities, solve for the unknown. Assume that interest is compounded annually and that all annuity amounts are received at the end of each period. (i = interest rate, and n = number of years) (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.)Present Value Annuity Amount i= n=1. ? 3000 8% 52. 242980 75000 ? 43. 161214 20000 9% ?4. 500000 80518 ? 85. 250000 ? 10% 4

Answer 1

Answer:

1)$11,978

2)9%

3)15 periods

4) 6%

5) $ 78,867.70

Explanation:

   PV       Annuity per period        rate         time  

1.     ?                  3,000                    8%             5

2. 242,980      75,000                     ?                4

3.   161,214       20,000                    9%              ?

4. 500,000       80,518                    ?                 8

5. 250,000           ?                        10%              4

1)

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 3,000.00

time 5

rate 0.08

$3000 \times \frac{1-(1+0.08)^{-5} }{0.08} = PV$

PV $11,978.1301

2)

solved using excel goal seek or financial calculator

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 75,000.00

time 4

rate 0.089998108 we set up the formula PV(A2;4,75000)

then we use goal seek to find which value of a2(which is the argument for rate) makes the formula equal to 242980

$75000 \times \frac{1-(1+0.0899981076987946)^{-4} }{0.0899981076987946} = PV$

PV $242,980.0000

3)

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C  $20,000.00

time n

rate 0.09

PV $161,214.0000

$20000 \times \frac{1-(1+0.09)^{-n} }{0.09} = 161214$

$(1+0.09)^{-n}= 1-\frac{161214\times0.09}{20000}$

$(1+0.09)^{-n}= 0.27453700$    

$-n= \frac{log0.274537}{log(1+0.09)$

-15.00004401

4)

same as (2) solved using excel

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 80,518.00

time 8

rate 0.06000009

$80518 \times \frac{1-(1+0.0600000899864588)^{-8} }{0.0600000899864588} = PV$

PV $500,000.0000

5)

$PV \div \frac{1-(1+r)^{-time} }{rate} = C$

PV 250,000

time 4

rate 0.1

$250000 \div \frac{1-(1+0.1)^{-4} }{0.1} = C$

C  $ 78,867.701