Question

b) Mr. Bert will retire in 15 years. What will be the total value of his investment when he retires?

You must show all of your steps to earn credit.

(2 points)

Answer 1

I don't have the rest of the problem (initial amount, interest rate, compounding frequency, or whether there are additional regular deposits). Please either paste the full problem (parts a and b) or give those numbers.

Meanwhile here are the formulas and the step-by-step process you should show, depending on the situation — use the one that matches the problem:

1) Single lump-sum P, interest rate r (as a decimal), compounded n times per year, for t years:
- Formula: A = P (1 + r/n)^(n t)
- Steps to show:
a. Write down P, r, n, t.
b. Compute the periodic rate r/n.
c. Compute the exponent n t.
d. Compute (1 + r/n)^(n t).
e. Multiply by P to get A.
f. Round to appropriate cents.

2) Single lump-sum, continuously compounded:
- Formula: A = P e^(r t)
- Steps:
a. Write P, r, t.
b. Compute r t.
c. Compute e^(r t).
d. Multiply by P to get A.

3) Regular end-of-period deposit (annuity), deposit PMT each period, interest rate i per period, N total periods:
- Formula (deposits at end of each period): A = PMT * [ (1 + i)^N − 1 ] / i
- If deposits are at the beginning of each period (annuity due): A = PMT * [ (1 + i)^N − 1 ] / i * (1 + i)
- Steps:
a. Convert annual rate to period rate i (and years to number of periods N).
b. Compute (1 + i)^N.
c. Compute numerator ( (1 + i)^N − 1 ).
d. Divide by i.
e. Multiply by PMT (and by (1 + i) if annuity due).

If you give me the numbers (P or PMT, r, compounding frequency, and t = 15 years), I will compute the total value and show every step.