Jacob is 25 yrs old and hopes to retire by 55. He invests $22,000 in an RRSP that earns a rate of 9.7% per annum, compounded quarterly. What will his investment be at age 55?

A=P(1+i)^n
2200(1+.097/4)^120
=$390067
to get the 120 I did 55-25=30 then * by 4 cause its compounded quarterly. But answer seems so high I'm questioning myself.

You are correct!

I got $390 067.17, the same as your answer.

You are looking at the power of compound interest.

To calculate the final investment value, we can use the compound interest formula: A = P(1 + r/n)^(nt), where:

A is the final investment value
P is the initial principal amount ($22,000 in this case)
r is the annual interest rate (9.7% or 0.097 as a decimal)
n is the number of times the interest is compounded per year (quarterly, so it would be 4)
t is the number of years (30 years, as Jacob wants to retire at age 55 and he is currently 25 years old)

Now, let's substitute the given values into the formula and solve for A:

A = 22000(1 + 0.097/4)^(4*30)
A = 22000(1 + 0.02425)^(120)
A = 22000(1.02425)^(120)
A ≈ $390,067 (rounded to the nearest dollar)

So, the investment will be approximately $390,067 when Jacob reaches the age of 55. And to answer your question about the calculation of the exponent, you were correct. Since the interest is compounded quarterly, you need to multiply the number of years (30) by 4 to obtain the total number of compounding periods (120).