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. How much cash is in Frank's IRA after 50 years? What must Gloria's annuity be for her IRA account balance to equal Frank's after 50 years?

Answer 1

For Frank,

R = 6.3%

Time n = 50 years

P = $1000

Cash in the IRA account of Frank (After 50 years) = P*((1+R)^n – 1)/R = 1000*(1.063^50 - 1)/.063

Cash in the IRA account of Frank = $320888.7

For Gloria

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

Effective annual interest rate = 5.127%

Let annuity for Gloria = A

Then,

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

320888.7 = A*218.0975

A = 320888.7/218.0975

A = $1471.308 or $1471.31

So, annuity for Gloria will be $1471.31 approx. to achieve the sum in 50 years that is achieved by Frank.