# PRESENT & FUTURE VALUE PROBLEMS?

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
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. 