Question

Problem 4-20 (algorithmic) Question Help men udel Compound interest is a very powerful way to save for your retirement. Saving a little and giving it time to grow is often more effective than saving a lot over a short period of time. To illustrate this, suppose your goal is to save $1 million by the age of 64. What amount of money will be saved by socking away $4,540 per year starting at age 26 with an 8% annual interest rate. Will you achieve your goal using the long term savings plan? What amount of money will be saved by socking away $16,423 per year starting at age 41 at the same interest rate? Will you achieve your goal using the short-term savings plan? equl Click the icon to view the interest and annuity table for discrete compounding when 8% per year The future equivalent of the long term savings plan is (Round to the nearest dollar)

Answer 1

Desirable savings = $1 million

Rate of interest = 8% compounded annually

Long term savings plan:

Amount invested per year = $4,540

Years invested = 38 years

Using compound interest formula: Future value = Amount Invested per year (1 + rate of interest)^{Years invested}

= 4,540 (1 + 0.8)³⁶ =84,558.75

Short term savings plan:

Amount invested per year = $16,423

Years invested = 23 years

Using compound interest formula: Future value = Amount Invested per year (1 + rate of interest)^{Years invested}

= 16,423 (1 + 0.8)²³ = 96,427.04

Target of $1 million would not be achieved either by short or long run savings plan.