When Raisel's son was born, she put $7,500 in an investment that earns 5.25% compounded quarterly. This investment will mature when her son turns 18 and will go straight into an annuity at 7.25% compounded and paying out monthly at the end of the period. The investment was to help pay for his 4-years of college. Find the size of these monthly payments received by Raisel's son during his college stay.

just change the appropriate numbers in the posting

http://www.jiskha.com/display.cgi?id=1270952022

They are the same question.

at age 18:

the amount of the investment = the present value of the annuity

6500(1.019375)^72 = x(1-0.0725/12^-48)/(0.0450/4)
19,177.84 = x(41.55860953)
x=461.46

is dis correct!!!

oh no...i mixed the queston

sry...ill try again!! oops

7500(1.013125)^72 = x(1-.0725/12^-48)/(.0725/12

19177.84 = x(41.55860953)
461.46 = x

is dis correct??

I got the same result to the penny!

good job!

To find the size of the monthly payments received by Raisel's son during his college stay, we need to calculate the future value of the initial investment and then use that amount to calculate the monthly annuity payments.

First, let's calculate the future value of the initial investment. The formula for calculating the future value of an investment compounded quarterly is:

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

Where:
FV = future value
PV = present value (initial investment)
r = annual interest rate (5.25% = 0.0525)
n = number of compounding periods per year (quarterly = 4)
t = number of years

Using the given values, we can plug them into the formula:

FV = $7,500 * (1 + 0.0525/4)^(4*18)
FV = $7,500 * (1 + 0.013125)^(72)
FV ≈ $15,560.50

So, the future value of the initial investment when her son turns 18 is approximately $15,560.50.

Now, let's calculate the monthly payments received from the annuity. The formula for calculating the monthly payments from an annuity is:

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

Where:
PMT = monthly payment
FV = future value (from the previous calculation)
r = annual interest rate (7.25% = 0.0725)
n = number of compounding periods per year (monthly = 12)
t = number of years (4 years of college)

Using the given values, we can plug them into the formula:

PMT = $15,560.50 * (0.0725/12) / ((1 + 0.0725/12)^(12*4) - 1)
PMT ≈ $380.14

Therefore, the size of the monthly payments received by Raisel's son during his college stay is approximately $380.14.