Question $1$:

I think when I was in elementary school in China, a Ping$-$Pong ball costs $4$ cents in $1988.$ It now costs $75$ cents in $2025.($All prices in this question are in Chinese currency. $1$ Yuan $=100$ cents.$)$

a$)$ What has been the annual price growth rate $($in $\%)$ in Ping$-$Pong ball in China in the last $37$ years?

b$)$ If a Chinese family has annual income of $1,500$ Yuan in $1988$ and $160,000$ Yuan in $2025,$ what is the annual growth rate $($in $\%)$ of this Chinese family$$s nominal income in the last $37$ years?

c$)$ What is the annual growth rate $($in $\%)$ of this Chinese family$$s real wealth in the last $37$ years, measured by their purchasing power of Ping$-$Pong balls?

Question $2$:

You have been wanting to buy a new car for some time. Now that you$$ve graduated from Albers with a job offer from a multinational company, you$$ve decided it$$s time to pull the trigger.

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a$.$ List the make and model of the car you want to purchase, along with the listing price. Provide the website addressfor your price information source $($e$.$g$.,$ dealership website, online marketplace link$).$

b$.$ After careful research, you$$ve narrowed down to two dealers that offer that model.

i$.$ Big Motor offers $$2,000$ price reduction for new college graduates like you. It requires $$5000$ down payment today, and provides a $5-$year financing plan with a $4\mathrm{.}5\%$ APR with monthly payment

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ii$.$ Auto King doesn$$t offer any price reduction. It also requires $$5,000$ down payment today and provides a $5-$year financing plan with a $3\mathrm{.}6\%$ APR with monthly payment.

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Using the price information you provided in Part a$,$ calculate the monthly loan payments for both Big Motor and Auto King. Based on your calculations, which dealer should you choose?

Question $3$:

First, provide three estimates based on your personal expectations:

$$ In how many years $($call it X$)$ do you think you can retire? X$=\_\_\_\_\_\_\_\_\_\_\_\_$ years

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$$ How many years $($call it Y$)$ do you expect to live after retirement? Y$=\_\_\_\_\_\_\_\_\_$ years

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$$ How much money $($call it Z$)$ do you think you$$ll need to spend per year in retirement to live comfortably? For you, Z$=$$$\_\_\_\_\_\_\_\_\_\_\_\_$

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Next, use your input of X$,$ Y and Z to solve the questions below.

You are trying to decide how much to save for retirement. Assume you plan to save $$15,000$ per year with the first investment made one year from now. You think you can earn $4\%$ per year on your investments and you plan to retire in X years, immediately after making your last $$15,000$ investment.

a$)$ How much will you have in your retirement account on the day you retire?

b$)$ If$,$ instead of saving $$15,000$ per year, you want to make one lump$-$sum investment today for your retirement that will result in the same retirement account balance you calculated in part a$),$ how much would that lump sum need to be$?$

c$)$ If you hope to live for Y years in retirement, how much can you withdraw every year in retirement $($staring one year after retirement$)$ so that you will just exhaust your savings with the last withdrawal $($assume her savings will continue to earn $4\%$ in retirement$)?$

d$)$ If$,$ instead, you decide to withdraw amount Z per year in retirement $($again with the first withdrawal one year after retiring$),$ how many years will it take until you exhaust your savings?

e$)$ Back to the retirement saving phase, if you plan to save $$15,000$ per year, but you want to retire in X years with $$3$ million in your investment account, how high of an annual return do you need to earn on your investments?

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