#$1$

Derek decides to buy a new car. The dealership offers him a choice of paying $$586\mathrm{.}00$ per month for $5$ years $($with the first payment due next month$)$ or paying some $$28,691\mathrm{.}00$ today. He can borrow money from his bank to buy the car. What interest rate makes him indifferent between the two options?

Attempts

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Answer format: Percentage Round to: $3$ decimal places $($Example: $9\mathrm{.}243\%,\%$ sign required. Will accept decimal format rounded to $5$ decimal places $($ex: $0\mathrm{.}09243))$

#$2$

Derek wants to withdraw $$11,119\mathrm{.}00$ from his account $3\mathrm{.}00$ years from today and $$12,225\mathrm{.}00$ from his account $15\mathrm{.}00$ years from today. He currently has $$2,308\mathrm{.}00$ in the account. How much must he deposit each year for the next $15\mathrm{.}0$ years? Assume a $6\mathrm{.}34\%$ interest rate. His account must equal zero by year $15\mathrm{.}0$ but may be negative prior to that.

Attempts R

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Answer format: Currency: Round to: $2$ decimal places.

#$3$

Derek currently has $$10,563\mathrm{.}00$ in an account that pays $4\mathrm{.}00\%.$ He will withdraw $$5,296\mathrm{.}00$ every other year beginning next year until he has taken $6\mathrm{.}00$ withdrawals. He will deposit $$10563\mathrm{.}0$ every other year beginning two years from today until he has made $6\mathrm{.}0$ deposits. How much will be in the account $25\mathrm{.}00$ years from today?

Attempts R

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Answer format: Currency: Round to: $2$ decimal places.

Derek can deposit $$292\mathrm{.}00$ per month for the next $10$ years into an account at Bank A$.$ The first deposit will be made next month. Bank A pays $12\mathrm{.}00\%$ and compounds interest monthly. Derek can deposit $$2,487\mathrm{.}00$ per year for the next $10$ years into an account at Bank B$.$ The first deposit will be made next year. Bank $B$ compounds interest

Attempts R

annually. What rate must Bank B pay for Derek to have the same amount in both accounts after $10$ years?

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Answer format: Percentage Round to: $4$ decimal places $($Example: $9\mathrm{.}2434\%,\%$ sign required. Will accept decimal format rounded to $6$ decimal places $($ex: $0\mathrm{.}092434))$

#$5$

Assume the real rate of interest is $3\mathrm{.}00\%$ and the inflation rate is $3\mathrm{.}00\%.$ What is the value today of receiving $13,315\mathrm{.}00$ in $7\mathrm{.}00$ years?

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Answer format: Currency: Round to: $2$ decimal places.

Attempts R