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Suppose you want to deposit money into an account where deposits increase every period after the first by some fixed number, g. For example:
• At the end of the first year, you deposit $R
• At the end of the second year, you deposit $R + g
• At the end of the third year, the previous year's deposit again increases by g, and so on…
As these deposits accumulate and earn compound interest, the total value of the annuity grows over time. To calculate the present value of such annuity, we use the following formula:
((1+i)^n [R+g(PV_(n−1) )]−[R+g(n−1)])/i
Recall: Present Value of Annuity (PV): (1−(1+i)^(−n))/i
Q. Marc wishes to build his wealth by investing money into an account that offers 4.5% annual interest. For the next five years, starting one year from today, he plans to deposit $2,000, and with each subsequent year increasing his deposits by $500 more than the year before. For example, after year 1, he deposits $2,000, after year-2, he deposits $2,500, and so on. By the end of the annuity, how much will Marc have accumulated, assuming the interest rate remains the same?