Question

Your company has a $125,000 liability it must pay 4 years from today. The company is opening a savings account so that the entire amount will be available when this debt needs to be paid. The plan is to make an initial deposit today and then deposit an additional $13,000 a year for the next 4 years, starting one year from today. The savings account pays a return of 8.00% compounded monthly. solve for the value

Question 8 options:

$43,284

$44,486

$45,688

$46,891

$48,093

Answer 1

Value of initial deposit required today to meet $125,000 in year 4:

Value of initial deposit required today is $48,093.34 or $48,093 (last option)

Steps:

1. First the future value of each of the yearly payment of $13,000 is computed using the excel function '=FV' as follows:

=FV(rate,nper,pmt,-pv) where

rate = 8%/12;

nper = for year 1 payment = 3 years remaining for 4th year * 12 = 3*12 = 36 months; for year 2 payment = 2 years remaining for 4th year * 12 = 2*12 = 24 months; for year 3 payment = 1 year remaining for 4th year * 12 = 1*12 = 12 months; for year 4 payment = 0 year remaining for 4th year * 12 = 0*12 = 0 months;

pmt = 0

pv = -$13,000

2. The total of all future value of $13,000 at year 4 is then deducted from $125,000 which is the future value of the today's initial deposit (which is $66,160.38)

3. The present of such value is then determined using the excel function '=PV' as follows:

=pv(rate,nper, pmt,-fv) where

rate = 8%/12

nper = 4 years * 12 months = 48

pmt = 0

fv = -$66,160.38