Question

Frank funds his IRA, with 6.3% effective annual interest, at $1,000 per year for 50 years. Gloria’s IRA account offers an interest rate of 5% compounded daily. A) How much cash is in Frank’s IRA after 50 years? B) What must Gloria’s annuity be for her IRA account balance to equal Frank’s after 50 years?

Answer 1

For Frank,

Interest Rate ( R ) = 6.3%

Time (n) = 50 yrs

P = $ 1000

After 50 Years Cash in the IRA account = P*((1+R)^n – 1)/R

= 1000*(1.063^50 - 1)/.063

Available Cash in Frank’s account after 50 years = $320888.7

For Gloria

Effective annual interest rate = (1+5%/365)^365 - 1

5.127 %

Let us assume that annuity for Gloria= A

Then,

320888.7 = A*(1.05127^50 - 1)/.05127

320888.7 = A*218.0975

A = $1471.308

So, annuity = $1471.308 in her IRA account balance to equal Frank’s after 50 years