Simple vs compound interest

a$.$ What is the amount of interest earned on $$2000$ for five years at $6\%$

simple interest per year

b$.$ Suppose you deposit $$1,000$ in a bank savings account that pays

interest at a rate of $8\%$ per ear. Assume that you do not withdraw the

interest earned at the end of each period $($year$)$ but instead let it

accumulate $(1)$ how much would you have at the end of year $3$ with

simple interests? $(2)$ how much would you have at the end of year $3$ with

compound interests?

c$.$ You deposit $$3,000$ in a savings account that earns $8\%$ simple interest

per year. How many years will it take to double your balance? If$,$ instead,

you deposit the $$3,000$ in another savings account that earns $7\%$

interest compounded yearly, how many years will it take to double your

balance?

APR vs APY

d$.$ If your credit card's APR is $24\%$ compounded monthly, what is the

effective annual interest rate that you are paying?

e$.$ Consider the following bank advertisement that appeared in an local

newspaper: $"$ open a liberty bank certificate of deposit $($CD$)$ and get a

guaranteed rate of return on as little as $\%500.$ It's a smart way to

manage your money for months. $($APR of $1$ st year is $2\mathrm{.}23\%$ and APY of

$1$ st year is $2\mathrm{.}25\%)"$ in this advertisement, no mention is made of specific

interest compounding frequencies. Find the compounding period for the

CD$.$

Present and$/$or Future values

f$.$ An amount of $$5,000$ is received today. Calculate the future value of

this amount after $5$ years with interest rate $6\mathrm{.}5\%.$

g$.$ You would like to have $$1M$ for your retirement at age $65$ years old.

Let's assume you are $25$ years old now. If $5\%$ of interest rate is fixed for

$40$ years $($APR$,$ compound yearly$),$ how much you need to save deposit

monthly?

h$.$ You are buying an item with $36$ monthly payments of $\%968$ each at an

APR of $10\%(i=$ APR $\frac{?}{12}$ months $=0\mathrm{.}833\%/$ month$).$ What would the

present value of the item?

i$.$ You are selling an item at $$30,000$ at $i=0\mathrm{.}833\%/$ month and $n=36$

months. How much does your customer need to pay monthly?