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.
at age 18:
the amount of the investment = the present value of the annuity
7500(1.013125)^72 = x(1-.0725/12^-48)/(.0725/12
19177.84 = x(41.55860953)
461.46 = x
is dis correct??
yes, I got the same answer to the penny!
good job!
thnx ^_^:D
To find the size of the monthly payments received by Raisel's son during his college stay, we need to calculate the value of the investment at age 18, which is the present value of the annuity.
First, let's calculate the value of the investment when Raisel's son turns 18. The formula for compound interest is:
A = P(1 + r/n)^(nt)
where:
A = final amount
P = principal (initial investment)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, Raisel invested $7,500 at an annual interest rate of 5.25% compounded quarterly for 18 years:
A = 7500(1 + 0.0525/4)^(4*18)
A = 7500(1.013125)^72
A ≈ 19,177.84
So, the value of the investment at age 18 is approximately $19,177.84.
Now, let's calculate the monthly payments received by Raisel's son during his college stay using the formula for the present value of an annuity:
PV = PMT * [(1 - (1 + r/n)^(-nt)) / (r/n)]
where:
PV = present value
PMT = monthly payment
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, the annuity pays out monthly at an annual interest rate of 7.25% compounded, which means the interest is compounded 12 times per year, and the payout lasts for 4 years (college stay):
19,177.84 = PMT * [(1 - (1 + 0.0725/12)^(-12*4)) / (0.0725/12)]
Let's solve this equation for PMT:
19,177.84 = PMT * (41.55860953)
PMT ≈ 461.46
Therefore, the size of the monthly payments received by Raisel's son during his college stay is approximately $461.46.
So, yes, your calculation is correct.