Finance - Annuities and Annuities Due

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Grant Productions borrowed a large sum from California Finance Company at 16.2% interest for 7 years. They must pay $1,406,231 annually. The present value of the loan is $6,560,485.97. Jeremy plans to save $2,479 annually for 8 years at a 10.1% rate to have $31,326.47 for a down payment. Ben will receive cash flows over 5 years totaling $49,368.39 at a 14.98% rate. An investment requiring $703 annual payments for 12 years at 6.7% has a present value of $5,674.09. Gregg will receive $50,000, $75,000, $125,

1.) Grant Productions has borrowed a huge sum from the California Finance Company at a rate of 16.2 percent for a seven-
year period. The loan calls for a payment of $1,406,231 each year beginning today. The company borrowed ______ $.

Note that this is an Annuity Due because the payments begin today.

R = 16.2%
CF = 1,406,231 / yr
t=7

CF 1
PV Annuity 1
r 1 r k PVAnnuityDue PVOrdinaryAn nuity 1 r
*k = the length of the annuity (7 years)

= [(1,406,231) / (.162)] * [ 1 – ]
= 5,645,857.115
= 5,645,857.115 * (1 + .162)

So PV = $6,560,485.97

2.) Jeremy Denham plans to save $2,479 every year for the next eight years, starting today. At the end of eight years,
Jeremy will turn 30 years old and plans to use his savings towards the down payment on a house. If his investment in a
mutual fund earns him 10.1 percent annually he will have $ in eight years when he will need the money to buy a house.

*This is Also an Annuity Due

R = 10.1%
CF = 2,479 / yr
t=8

CF k
FV Annuity 1 r 1
r
= 2,479 / .101 [( 1 + .101 ) ^ 8 – 1 ]
= 28,452.74068
= 28,452.74068 * (1 + .101)
= $31,326.47

3.)Ben Woolmer has an investment that will pay him the following cash flows over the next five years: $7,512, $5,845,
$9,203, $8,574, and $5,329. If his investments typically earn 14.98 percent, the future value of this set of cash flows at the
end of five years is ________$.

*In this problem, it is much easier to use your calculator because you can collapse this series of cash flows in to one
cash flow and then find its value at any point in time. Otherwise you need to take each individual cash flow and
move it ahead to the 5th year (except for cf 5). Ex) CF1*(1+r)^4 + CF2*(1+r)^3 + CF3*(1+r)^2 +CF4*(1+r)^1 + CF5

R = 14.98%
t=5
= 7,512 = 5,845 = 9,203 = 8,574 = 5,329
FV = $49,368.39

4.) An investment opportunity requires a payment of $703 for 12 years, starting a year from today. If your required rate of
return is 6.7 percent, the value of the investment is _______ $ today.

R = 6.7%
CF = 703 / yr
t = 12

Use this: PV CF /(1 r ) CF /(1 r ) 2 CF /(1 r )3 ?
Or, use your calculator because it is much easier….

PV Annuity = $5,674.09

5.)Gregg is expecting cash flows of $50,000, $75,000, $125,000, and $250,000 from an inheritance over the next four
years. If she can earn 11 percent on any investment that she makes, what is the present value of her inheritance? (Round
to the nearest dollar.)

R = 11%
= 50,000 = 75,000 = 125,000 = 250,000
t=4

This is the same as number 3, except this time you are discounting the cash flows back to year zero. You can brute
force it by manually punching it in your calculator:

PV CF /(1 r ) CF /(1 r ) 2 CF /(1 r )3 ?
Or use the net present value (npv) function which is much quicker, however, judging by these problems, you haven’t
gotten to that yet.

PV Annuity = $361,998.39

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Finance - Annuities and Annuities Due

1. 1.) Grant Productions has borrowed a huge sum from the California Finance Company at a rate of 16.2 percent for a seven- year period. The loan calls for a payment of $1,406,231 each year beginning today. The company borrowed ______ $. Note that this is an Annuity Due because the payments begin today. R = 16.2% CF = 1,406,231 / yr t=7 CF 1 PV Annuity 1 r 1 r k PVAnnuityDue PVOrdinaryAn nuity 1 r *k = the length of the annuity (7 years) = [(1,406,231) / (.162)] * [ 1 – ] = 5,645,857.115 = 5,645,857.115 * (1 + .162) So PV = $6,560,485.97 2.) Jeremy Denham plans to save $2,479 every year for the next eight years, starting today. At the end of eight years, Jeremy will turn 30 years old and plans to use his savings towards the down payment on a house. If his investment in a mutual fund earns him 10.1 percent annually he will have $ in eight years when he will need the money to buy a house. *This is Also an Annuity Due R = 10.1% CF = 2,479 / yr t=8 CF k FV Annuity 1 r 1 r = 2,479 / .101 [( 1 + .101 ) ^ 8 – 1 ] = 28,452.74068 = 28,452.74068 * (1 + .101) = $31,326.47 3.)Ben Woolmer has an investment that will pay him the following cash flows over the next five years: $7,512, $5,845, $9,203, $8,574, and $5,329. If his investments typically earn 14.98 percent, the future value of this set of cash flows at the end of five years is ________$. *In this problem, it is much easier to use your calculator because you can collapse this series of cash flows in to one cash flow and then find its value at any point in time. Otherwise you need to take each individual cash flow and move it ahead to the 5th year (except for cf 5). Ex) CF1*(1+r)^4 + CF2*(1+r)^3 + CF3*(1+r)^2 +CF4*(1+r)^1 + CF5 R = 14.98% t=5 = 7,512 = 5,845 = 9,203 = 8,574 = 5,329 FV = $49,368.39

2. 4.) An investment opportunity requires a payment of $703 for 12 years, starting a year from today. If your required rate of return is 6.7 percent, the value of the investment is _______ $ today. R = 6.7% CF = 703 / yr t = 12 Use this: PV CF /(1 r ) CF /(1 r ) 2 CF /(1 r )3 ? Or, use your calculator because it is much easier…. PV Annuity = $5,674.09 5.)Gregg is expecting cash flows of $50,000, $75,000, $125,000, and $250,000 from an inheritance over the next four years. If she can earn 11 percent on any investment that she makes, what is the present value of her inheritance? (Round to the nearest dollar.) R = 11% = 50,000 = 75,000 = 125,000 = 250,000 t=4 This is the same as number 3, except this time you are discounting the cash flows back to year zero. You can brute force it by manually punching it in your calculator: PV CF /(1 r ) CF /(1 r ) 2 CF /(1 r )3 ? Or use the net present value (npv) function which is much quicker, however, judging by these problems, you haven’t gotten to that yet. PV Annuity = $361,998.39

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