Dominique has just turned 65 and she has deposited her annual payment of $20,000 into her retirement account. She made her first such saving deposit into this fund on her 35th birthday. Dominique has also retired and wants to figure out how much money she has in her retirement account for her retired life. You are Dominique's friend who knows finance. How much is Dominique's savings worth today given that the fund has earned an annual return of 5.5%? (Enter just the number without the $ sign or a comma; round off decimals.)
($1,448,709.56)
To calculate Dominique's savings worth today, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = Final amount (savings worth today)
P = Principal amount (initial deposit)
r = Annual interest rate (as a decimal, in this case 5.5% = 0.055)
n = Number of times interest is compounded per year (assuming once annually, so n = 1)
t = Number of years the money is invested (in this case, from age 35 to age 65, so t = 30)
Plugging in the values:
A = $20,000(1 + 0.055/1)^(1*30)
Simplifying,
A = $20,000(1 + 0.055)^30
Using a calculator, we find:
A ≈ $20,000(1.055)^30
A ≈ $20,000(2.4709)
A ≈ $49,418.00
Therefore, Dominique's savings worth today is approximately $49,418.