Problema Solution
Saul invested an average of $425 per month since age 30 in various securities for his retirement savings. His investments averaged a 3.5% annual rate of return until he retired at age 60. Given the same monthly investment and rate of return, how much more would Saul have in his retirement savings had he started investing at age 20? Assume monthly compounding
Answer provided by our tutors
The formula for the compound amount is
A = P (1 + (i/n))^ (n*t)
in our case
P = $425
i = 0.035 (3.5%)
n = 12 (interest compounded monthly)
t = 30 years
A = 425*((1 + (0.035/12))^360)
A = $1,212.65 approximately
After 30 years he will have $1,212.65 retirement savings.
if t = 40 that is if he started investing at the age of 20 and since 60 - 20 = 40 we have
A = 425*((1 + (0.035/12))^480)
A = $1,719.95 approximately
After 30 years he will have $1,719.95 retirement savings.
Since we need to find how much more retirement savings would he had if he started investing at age 20 we need to find the difference between $1,719.95 and $1,212.65 that is
1,719.95 - 1,212.65 = $507.3
Saul would have $507.3 in his retirement savings had he started investing at age 20.