Answer:
1. Lulu started saving $200/month in a 401(k) earning 6% interest compounded monthly when she was 45 years old. How much will be in her account when she retires at age 65?
Lulu made 12 x 20 = 240 payments
to calculate how much she earned we can use the future value of ordinary annuity formula:
FV annuity = payment x {[(1 + r)ⁿ - 1] / i} = $200 x {[(1 + 0.5%)²⁴⁰ - 1] / 0.5%} = $200 x 462.04 = $92,408.18
2. How much money did Lulu deposit into her account over the course of the 20 years?
240 x $200 = $48,000
3. What dollar amount of interest did her account earn?
$92,408.18 - $48,000 = $44,408.18
4. Murphy started putting $100/month into his 401(k) earning 6% APR when he was 25 years old. How much will be in his account when he retires at age 65, if interest is compounded monthly?
480 payments, again we use the same formula as in (1):
FV annuity = $100 x {[(1 + 0.5%)⁴⁸⁰ - 1] / 0.5%} = $100 x 1,991.49 = $199,149.07
5. How much money did Murphy deposit into his account over the course of the 40 years?
480 x $100 = $48,000
6. What dollar amount of interest did his account earn?
$199,149.07 - $48,000 = $151,149.07
7. Murphy's account earned how much more interest than Lulu's account?
$151,149.07 - $44,408.18 = $106,740.89
