Question

Instead of buying Starbucks (or boba), I decide to start saving the money. Assume it's $4/ drink with an average of 3 times per week. How much will we accumulate if we invest these funds for 40 years at 8% (for simplicity assume funds are deposited once per year at the end of the year)>

Answer 1

Solution:

As per the information given in the question we have

Savings per drink = $ 4 ; No. times savings is made in a week = 3 times   ; No. of weeks in a year = 52 weeks ;

Thus total savings in year = Savings per drink * No. times savings is made in a week * No. of weeks in a year

= $ 4 * 3 * 52 = $ 624

Thus Periodic Deposit i.e., Fixed amount of Annual deposit = $ 624

The formula for calculating the Future value of savings at the end of n years is

= P * [ [ ( 1 + r ) n - 1 ] / r ]

Where

P = Periodic Deposit i.e., Fixed amount of Annual deposit ; r = rate of interest   ; n = no. of years ;

A per the information given in the question we have

P = $ 624 ; r = 8 % = 0.08   ;   n = 40 ;

Applying the above values in the formula we have:

= 624 * [ [ ( 1 + 0.08 ) 40   - 1 ] / 0.08 ]                        

= 624 * [ [ ( 1.08 ) 40   - 1 ] / 0.08 ]

= 624 * [ [ 21.724521 – 1 ] / 0.08 ]

= 624 * [ 20.724521 / 0.08 ]

= 624 * 259.056519

= $ 161,651.267675

Thus the amount that is accumulated if the funds are invested for 40 years at 8 % = $ 161,651.27

Note: The value of ( 1.08 ) 40   is calculated using the Excel function =POWER(Number,Power)

=POWER(1.08,40)= 21.724521