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Annuities, Compounds Interest and Sinking Funds

Joseph wants to deposit $1,500 at year-end for 35 years at 8%. What will his result be? If Joseph deposits $1,000 at the end of each year for the next 5 years at 8% compounded annually, $1,500 at the end of years 6-10 at 8% compounded annually, and $2,000 at the end of years 11-35 at 5% compounded annually, how much would he accumulate at the end of 35 years? Assume that any balances from earlier deposits would continue to earn the same rate of annual interest.

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Formula for calculation of future value of annunity=
S = R[ (1+i)^n -1]/i
Where, S = future valuation
R = periodic payment
i = Interest rate per period
n= number of periods
Here, R= $1500
n = 35
So, S= 1500[ {1+(8/100)}^35 -1]/(8/100) = $258475.21

In the first case, R1= $1000

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