Question

If you won a $184,443 lottery prize at age 23 and invested it at 2.3% compounded 9 times a year, how much would it be worth if you retired at age 65?

a) $348,910.23
b) $219,678.45
c) $684,512.37
d) $506,843.21

Answer 1

la correcta es el inciso a

Answer 2

To calculate the future value of a lottery prize with compound interest, use the formula: FV = P × (1 + r/n)^(nt). For this question, the future value is approximately $506,843.21, which corresponds to option d).

Step-by-step explanation:

The question involves compound interest, which is a key concept in personal finance and investment strategies. To calculate the future value of the $184,443 lottery prize invested at 2.3% compounded 9 times a year until retirement at age 65, we use the compound interest formula:

Future Value (FV) = P × (1 + r/n)nt

Here, P is the initial principal balance, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years the money is invested.

For this question:

P = $184,443

r = 2.3% or 0.023

n = 9

t = 65 - 23 = 42 years

Plugging these values into the formula gives us:

FV = $184,443 × (1 + 0.023/9)9 × 42

Calculating this, the future value comes out to be approximately $506,843.21, therefore the correct answer is option d) $506,843.21.