Question

| A 20 year old person saves $400.00 per month for 10 years in a retirement account that is paying 8%. At the end of the 10 years, the person leaves that amount in the same account (i.e. paying the same interest, 1 compounding, etc.) until retiring at age 65. How much money will be in the person's account? Over the course of the entire investment, how much interest is earned by this person? This problem calls for a two part calculation. Find the amount accumulated over the first ten years and then calculate the final amount in the account. Interest is calculated from start to finish. Are the calculations different? Think about this and consult the table on page 163.

This is for my Math for Liberal Arts class; for chapter: Mathematics of Finance.

Answer 1

ASSUMING MONTHLY COMPOUNDING

Amount accumulated over the first ten years=monthly amount/(rate/12)*((1+rate/12)^(12*10)-1)=400/(8%/12)*((1+8%/12)^(12*10)-1)=73178.41407

Final amount=present value*(1+r/m)^(m*t)=73178.41407*(1+8%/12)^(12*35)=1192262.963

Interest=Final amount-total contributions=1192262.963-400*12*10=1144262.963