Question

You just won a lottery - CONGRATULATIONS! Your parents have always told you to plan for the future, so since you already have a well- paying job you decide to invest rather than spend your lottery winnings. The payment schedule from the lottery commission is $100,000 after taxes at end of year one and 19 more payments of exactly $100,000 after taxes in equal annual end- of- the- year deposits (i.e., the first of the next 19 deposits is one year from today) into your account pays 7% compounded annually. How much money will be in your account after the last deposit is made?

Answer 1

Answer: $2,027,087.791

Explanation:

Given that,

Lottery commission = $100,000

Remaining 19 payments annually = $100,000

Compounded payment = 7%

Total compounded payment till end:

$A(t)=A_{0}(1+\frac{r}{n}) ^{nt}$

Where,

A0 = Compounded payment at first deposit = $7,000

t = Total time in years = 20 years

n = No. of compounding periods per year = 1

r = Nominal annual interest rate expressed as a decimal = 0.07

Therefore,

$A(20)=7,000(1+\frac{0.07}{1})^{20}$

               = 7,000 × 3.8696

               = $27,087.79

After 20 years,

Total amount deposited will be = $20,00,000 + $27087.79

                                                     = $2,027,087.791