Question

An individual deposited $3000 at the beginning of each year into an IRA account which earns 7% compounded quarterly. If the payments began on January 1, 2020 and will end on January 1, 2045, determine the balance on January 1, 2046. ($227,118.93) Cannot use Excel.

Answer 1

Effective rate of interest = (1+r/n)^n -1
n= number of periods in a year
r = interest rate
= (1+0.07/4) ^4 - 1
=7.185903%
Future Value of an Annuity Due
= C*[(1+i)^n-1]/i] * (1+i)
Where,
c= Cash Flow per period
i = interest rate per period =7.185903
n=number of period =2046-2020 =26
= $3000[ (1+0.07185903)^26 -1 /0.07185903] * (1 +0.07185903)
= $3000[ (1.07185903)^26 -1 /0.07185903] * 1.07185903
= $3000[ (6.0755 -1 /0.07185903] * 1.07185903
= $2,27,118.93