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$6.$ Future value calculations

Future Value Calculations

Lexi and Luke are still sitting together, with their notebooks and textbooks open, in a booth at a nearby coffee shop. They$$ve been working practice problems from Dr$.$ Smith$$s personal finance class. Help Lexi and Luke complete the following three problems in their homework assignment.

Problem $1.$ Within the month, Joshua is taking a new job and moving to a city with an outstanding rapid transit system. He intends to sell his car for $$12,500$ and invest the money by placing it in a savings account. The account will pay $5\%$ per year in compound interest, and he wants to keep the funds on deposit for four years.

You can use the following table of Future Value Interest Factors:

Interest Factors$$Future Value of a Single Amount

Periods

$4\mathrm{.}50\%$

$5\mathrm{.}00\%$

$5\mathrm{.}50\%$

$6\mathrm{.}00\%$

$6\mathrm{.}50\%$

$7\mathrm{.}00\%$

$7\mathrm{.}50\%$

$8\mathrm{.}00\%$

$21\mathrm{.}09201\mathrm{.}10251\mathrm{.}11301\mathrm{.}12361\mathrm{.}13421\mathrm{.}14491\mathrm{.}15561\mathrm{.}1664$

$31\mathrm{.}14121\mathrm{.}15761\mathrm{.}17421\mathrm{.}19101\mathrm{.}20791\mathrm{.}22501\mathrm{.}24231\mathrm{.}2597$

$41\mathrm{.}19251\mathrm{.}21551\mathrm{.}23881\mathrm{.}26251\mathrm{.}28651\mathrm{.}31081\mathrm{.}33551\mathrm{.}3605$

$51\mathrm{.}24621\mathrm{.}27631\mathrm{.}30701\mathrm{.}33821\mathrm{.}37011\mathrm{.}40261\mathrm{.}43561\mathrm{.}4693$

$61\mathrm{.}30231\mathrm{.}34011\mathrm{.}37881\mathrm{.}41851\mathrm{.}45911\mathrm{.}50071\mathrm{.}54331\mathrm{.}5869$

At the end of his investment period, Joshua expects to have an accumulated balance of in his savings account. $($Note: Round your answer to the nearest whole dollar.$)$

Problem $2.$ Jacob is currently taking a course in personal finance and has learned the benefits of both starting a savings plan and starting it early. Therefore, he has decided to save $$1,440$ per year in an account that pays $6\%.$ He plans to open the account tomorrow and will make deposits at the end of each year, including this year, for the next $15$ years. $($Note: Round your answer to the nearest whole dollar.$)$

You can use the following table of Future Value Interest Factors:

Interest Factors$$Future Value of an Annuity

Periods

$5\mathrm{.}00\%$

$6\mathrm{.}00\%$

$7\mathrm{.}00\%$

$8\mathrm{.}00\%$

$1012\mathrm{.}577913\mathrm{.}180813\mathrm{.}816414\mathrm{.}4866$

$1521\mathrm{.}578623\mathrm{.}276025\mathrm{.}129027\mathrm{.}1521$

$2033\mathrm{.}066036\mathrm{.}785640\mathrm{.}995545\mathrm{.}7620$

$2547\mathrm{.}727154\mathrm{.}864563\mathrm{.}249073\mathrm{.}1059$

By the end of his investment period, he will have saved $.$

Problem $3.$ Joshua$$s grandfather is pleased that his grandson is learning to save. To further encourage the practice, he has offered to give his grandson a gift of $$3,000$ per year for each year that Joshua keeps the proceeds from the sale of his car invested$$presumably for the next four years. He has opened a new savings account that will pay a rate of $8\%$ per year. $($Note: Round your answer to the nearest whole dollar.$)$

You can use the following table of Future Value Interest Factors:

Interest Factors$$Future Value of an Annuity

Periods

$5\mathrm{.}00\%$

$6\mathrm{.}00\%$

$7\mathrm{.}00\%$

$8\mathrm{.}00\%$

$22\mathrm{.}05002\mathrm{.}06002\mathrm{.}07002\mathrm{.}0800$

$33\mathrm{.}15253\mathrm{.}18363\mathrm{.}21493\mathrm{.}2464$

$44\mathrm{.}31014\mathrm{.}37464\mathrm{.}43994\mathrm{.}5061$

$55\mathrm{.}52565\mathrm{.}63715\mathrm{.}75075\mathrm{.}8666$

$66\mathrm{.}80196\mathrm{.}97537\mathrm{.}15337\mathrm{.}3359$

If Joshua$$s grandfather makes deposits of $$3,000$ per year into the new savings account for each of the next four years and the deposits are made at the end of each year, then the new savings account will have a total balance of at the end of year four.