Use the formula for sum of series to find payment information

Question

Around January 1, 1993, Barbara Streisand (a singer/actress for those of you too young to know!)
signed a recording contract with Sony Corporation for $2 million each year for 10 years. Suppose the
first payment of $2 million was made on the day of signing the deal and all other payments to her were
made on the first day of each subsequent year. Suppose all payments were directed into her bank
account earning 4% a year, compounded semi-annually.

 

 i) Assuming she never made any withdrawals from the account, how much money was in
her account on the day the last payment was made? (Be sure to use the formula for
finding sum of a series.)

 

 ii) What was the present discounted value of the recording contract to her the day it was
signed? (Be sure to use the formula for finding sum of a series)

Answer 1

For compound interest with regular deposits:

 

A = d[(1 + r/n)^nt - 1](n / r), where A = final amount, d = regular deposit, r = interest rate, n = number of calculations per year, and t = number of years.