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Assume that your parents wanted to have 120,000 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 12.0 %12.0% 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 $ 160 comma 000$160,000 saved just in​ case, how much would they have to save each year to reach their new ​goal?

Respuesta :

Answer:

save each year to reach their​ goal is $2152.48  

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

Explanation:

given data

amount saved = 120,000

Rate of Interest earned =  12.0 %

time = 18th birthday  

solution

we consider here annual savings is =  P

we use here formula for future value of annuity  that is

future value of annuity = P ×  [tex]\frac{(1+r)^n -1 }{r}[/tex]    ................1

here r is rate and n is time period

put her value

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

solve we get P = $2152.48

save each year to reach their​ goal is $2152.48  

and

for $160,000 at 18th Birthday

we consider here  annual savings =  P

so from equation 1

we put here value

future value of annuity = P ×  [tex]\frac{(1+r)^n -1 }{r}[/tex]

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

solve and we get P = $2869.97

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

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