Question

assume that your parents wanted to have saved for college by your 18th birthday and they started saving on your first birthday. they saved the same amount each year on your birthday and earned per year on their investments. a. how much would they have to save each year to reach their​ goal? b. if they think you will take five years instead of four to graduate and decide to have saved just in​ case, how much would they have to save each year to reach their new​ goal? question content area bottom part 1 a. how much would they have to save each year to reach their​ goal? to reach the goal of ​, the amount they have to save each year is ​$ enter your response here. ​(round to the nearest​ cent.)

Answer 1

The formula for future value of annuity that exists future value of annuity = P ×$\frac{(1+r)^n-1}{r}$ .

Save each year to reach their​ goal exists $2152.48

Save each year to reach their new ​goal exists $2869.97

What is meant by future value of annuity?

The worth of a series of recurrent payments at a specific future date, assuming a specific rate of return, or discount rate, is the future value of an annuity. The future value of the annuity increases with the discount rate.

Given: amount saved = 120,000

Rate of Interest earned = 12.0 %

time = 18th birthday

Where, annual savings = P

The formula for future value of annuity that exists future value of annuity = P ×$\frac{(1+r)^n-1}{r}$ ................(1)

where r exists rate and n exists a time period

put her value

$ 120,000 = P × $\frac{(1+0.12)^{18}-1}{0.12}$

= $ 2152.48

Save each year to reach their goal exists $ 2152.48 and for $ 160,000 on 18 th Birthday

we consider here annual savings = P

From (1),

Future value of annuity = P × $\frac{(1+r)^n-1}{r}$

$ 160,000 = P ×  $\frac{(1+0.12)^{18}-1}{0.12}$

P = $2869.97

Therefore, Save each year to reach their​ goal exists $2152.48

save each year to reach their new ​goal is $2869.97

To learn more about future value of annuity refer to:

brainly.com/question/27011316

#SPJ4