PRESENT & FUTURE VALUE PROBLEMS?

I can't get the right answers to the following problems, please help.
1. mr paul plans to establish an annuity agreement whereby the four children would each receive $3,700 on December 31 of the yrs 2004 to 2018, inclusive. variation in the interest rate during that period are:
12/31/03-12/31/08=12%
12/31/08-12/31/14=11%
12/31/14-12/31/18=9%
COMPUTE the amount mr paul must invest on 12/31/03 to assure the annual payment to his children? THE ANSWER IS $103,425

FUTURE VALUE
Brookes invest $10,00 at the starting point of the next 2 yrs, 10%. how much will brooks have in 2 yrs, if interest is compunded semi annualy? THE ANSWER IS $23,180
Answers:
Let's meet head-on the second question:
What is the future value of $10,000 invested at 10%,
compounded semi-annually for 2 years?

FV = P * (1 + r/n)^(n*t)

Where:
FV = Future Value (what you're solving for)
P = Principal (assuming the amount invested is $10,000, not $10,00)
r = interest rate (expressed as a decimal = .10)
n = number of compoundings per year (2)
t = time surrounded by years (2)

FV = P * (1 + r/n)^(n*t)
FV = $10,000 * (1 + .10/2)^(2*2)
FV = $10,000 * (1 + .05)^4
FV = $10,000 * (1.05)^4
FV = $10,000 * (1.21550625)
FV = $12,155.06 ← (Correct answer)

It's not possible for $10,000 to mature into $23,180 in two years at 10%.
(It would pocket 8.61551 years for this to happen).
There's obviously something wrong with the problem as given.
Check with your professor.

Annuities are another globe of wax... which I don't have the time to explain right now.
Chances are that if you didn't get the correct answer,
your classmates didn't any.

Sounds like your professor is losing his edge.

Good luck in your studies,
~ Mitch ~ Source(s): Business / Accounting Major


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