Homework

Chapter $5$: Time Value of Money.

Problem $8$: Isabella deposited $$1,400$ in a savings account at her bank. Her account will earn an annual simple interest rate of $6\mathrm{.}6\%.$ If she makes no additional deposits or withdrawals, how much money will she have in her account in $13$ years?

Problem $9$: Now, assume that Isabella's savings institution modifies the terms of her account and agrees to pay $6\mathrm{.}6\%$ in compound interest on her $$1,400$ balance. All other things being equal, how much money will Isabella have in her account in $13$ years?

Problem $10$: Suppose Isabella had deposited another $$1,400$ into a savings account at a second bank at the same time. The second bank also pays a nominal $($or stated$)$ interest rate of $6\mathrm{.}6\%$ but with quarterly compounding. Keeping everything else constant, how much money will Isabella have in her account at this bank in $13$ years?

Problem $11$: If a security currently worth $$2,000$ will be worth $$3,524\mathrm{.}68$ five years in the future, what is the implied interest rate the investor will earn on the security$-$assuming that no additional deposits or withdrawals are made?

Problem $12$: How many years will it take an investment of $$40,000$ at the interest rate of $8\mathrm{.}00\%,$ compounded annually, to reach a value of $$56,554\mathrm{.}46-$assuming that no additional deposits or withdrawals are made during this time?

Problem $13$: If you invest $$1$ today at $15\%$ annual compound interest for $82\mathrm{.}3753$ years, you'll end up with $$100,000.$ True or False?

Problem $14$: When equal payments are made at the end of each period for a certain time period, they are treated as an annuity due. True or False?

Problem $15$: Ashley has started saving at the end of each year, she deposits $$1,060$ in her bank account, which pays her $7\%$ interest annually. She wants to keep saving for two years. Ashley's savings are an example of an annuity. How much money will Ashley have at the end of two years?

Problem $16$: If Ashley deposits the money at the beginning of every year and everything else remains the same, she will save $$........q,$ by the end of two years.

Problem $17$: Ryan inherited an annuity worth $$3,280\mathrm{.}16$ from his uncle. The annuity will pay him five equal payments of $$800$ at the end of each year. The annuity fund is offering a return of $q,\%.$