Question

If a person spends $20 a week on coffee (assume $1,000 a year), what would be the future value of that amount over 15 years if the funds were deposited in an account earning 2 percent? Use Exhibit 1-B. (Round time value factor to 3 decimal places and final answer to 2 decimal places.)

future value=

Answer 1

Annual Spends on Coffee = $1,000

Spends in a week (P) = $20

thus,

No. of week in year = 1000/20 = 50

No. of week in 15 years (n) = 50*15 = 750

Interest rate (weekly)(i) = 0.02/50 = 0.0004

Now, we can calculate the Future value (FV) if funds deposited in an account with following equation -

FV = P* FVIAF(in)

where,

FVIAF = Future value interest annuity factor

FVIAF(in) = (1+i)(1 – (1+i))

putting the value-

(1 +0.0004)(1 - (1+0.0004)750 FVIAF(0.0004, 750) = 4 -0.0004

FVIAF(0.0004, 750) = (1.0004) (1 - 1.3497778400672) -0.0004

FVIAF(0.0004, 750) = (1.0004)(-0.3497778400672) -0.0004

FVIAF(0.0004, 750) = -0.349917751203 -0.0004

FVIAF(0.0004, 750) = 874.794

Thus,

FV = P* FVIAF(in)

FV = 20 * 874.794

FV = $17,495.89

Note - It is assumed that deposit are made at beginning of the week to solve above question. However, Future value of deposit would be $17,488.90 if deposit are made at end of week.

Hope this will help, please do comment if you need any further explanation. Your feedback would be appreciated.