Determine a onetime investment that would result from saving

Determine a one-time investment that would result from saving money over one calendar year by cutting one personal habit, such as buying expensive coffee.

Find the account value based on the compound interest formula after N years, if the amount is compounded annually. Then using the formula, determine the account value in 10 years, 20 years, 30 years, and 40 years if the money were invested in a plan that grew 8% ...or at a rate of your choice ... annually. In how many years would you have more than $100,000 in this account?

THEN

Find the future value of an annuity formula based on geometric SERIES that can be used to determine the account value of that same investment but instead invested once a year after N years, if the amount is compounded yearly. Repeat the same instructions above.

Solution

compound interest formula is

A=P+[1+r/n]^nt

P is principal amount

expensive coffee per year $3000*12=$36000

r=6/100=0.06

n=1

t =10

A=36000[1+0.06]¹⁰

   =36000[1.06]¹⁰

=36000[1.7908]=64468.8

after 20 years

compound interest formula is

A=P+[1+r/n]^nt

here value of t=20 all the remaining values are same as for 10 years

A=36000[1+0.06]²⁰

   =36000[1.06]²⁰

=36000[3.2071]=151455.6

after 20 years the account value is 151,455.6

after 30 years

A=36000[1+0.06]³⁰

   =36000[1.06]³⁰

=36000[5.7434]=242762.8

after 30 years

A=36000[1+0.06]³⁰

   =36000[1.06]³⁰

=36000[5.7434]=264765

after 30 the amount is 264.756

so after 20.30,40 years the amount increasesand amount is more then $100,000