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4. Steven is able to invest $500 a month for 10 years in an account that pays 7% per year. Hethen stops making payments and lets the amount in the account continue to grow andcompound continuously for 20 years. How much is in the account at the end of this 30 yearperiod?a. How much is in the account after 10 years?b. How much is in the account at the end of this 30 year period?c. What was the total amount that Steven invested in this account?d. What was the interest that Steven earned on this account over this 30 year period?

Respuesta :

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(a) For the first 10 years; we apply annuity formula;

[tex]\begin{gathered} PV=p\times\frac{1-(1+r)^{-n}}{r} \\ PV=present\text{ }value\text{ }of\text{ }an\text{ }ordinary\text{ }annuity,\text{ }P=value\text{ }of\text{ }each\text{ }payment,\text{ }r=interest\text{ }rate\text{ }per\text{ }period,\text{ }n=number\text{ }of\text{ }periods \end{gathered}[/tex][tex]\begin{gathered} p=500\times12=\text{ \$6000} \\ r=7\text{\%} \\ n=10years \end{gathered}[/tex][tex]undefined[/tex]

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