Question

 Upon graduating from college 40 years​ ago, Dr. Nick Riviera was already planning for his retirement. Since​ then, he has made deposits into a retirement fund on a semiannually basis in the amount of ​$600. Nick has just completed his final payment and is at last ready to retire. His retirement fund has earned 7 percent compounded semiannually.

Use five decimal places for the periodic interest rate in your calculations.

a.  How much has Nick accumulated in his retirement​ account?

b. In addition to​ this, 20 years ago Nick received an inheritance check for ​$25,000 from his beloved uncle. He decided to deposit the entire amount into his retirement fund. What is his current balance in the​ fund?

a.  The amount Nick has accumulated in his retirement account is ​$___

Answer 1

a

FVOrdinary Annuity = C*(((1 + i/(f*100))^(n*f) -1)/(i/(f*100)))

C = Cash flow per period

i = interest rate

n = number of payments I f = frequency of payment

FV= 600*(((1+ 7/200)^(40*2)-1)/(7/200))

FV = 251584.1

Using Calculator: press buttons "2ND"+"FV" then assign

PMT =-600

I/Y =7/2

N =40*2

PV = 0

CPT FV

Using Excel

=FV(rate,nper,pmt,pv,type)

=FV(7/(2*100),2*40,-600,,)

b

EAR = [(1 +stated rate/no. of compounding periods) ^no. of compounding periods - 1]* 100

? = ((1+7/(2*100))^2-1)*100

Effective Annual Rate% = 7.1225

Future value = present value*(1+ rate)^time

Future value = 25000*(1+0.071225)^20

Future value = 98981.49

Using Calculator: press buttons "2ND"+"FV" then assign

PV =-25000

I/Y =7.1225

N =20

PMT = 0

CPT FV

Using Excel

=FV(rate,nper,pmt,pv,type)

=FV(0.071225,20,,-25000,)

Total = 251584.1+98981.49

=

350565.59