$1)$ Harry, Jerry, Mary and Cari all plan to retire at age $67.$ Each of them contributes $$425$ per month in

an ordinary annuity paying $7\mathrm{.}2\%$ interest compounded monthly. Answer the following. Round all

dollar answers to the nearest hundred dollars, and round all percent answers to the nearest

whole$-$number percent. To make sure you are off to a good start, I did $1$a$)$ for you. Before

attempting $1$b$,$ c$,$ d$,$ you should try $1$a$)$ yourself to ensure you are doing the problems correctly.

a$)$ Harry starts his retirement account at age $57.$

$$ How much will be in the account when he retires? $$74,400$

$$ How much of the final amount is money he put in$?$ $$51,000$

$$ How much of the final amount is interest he earned? $$23,400$

$$ What percent of the final amount is interest he earned? $31\%$

b$)$ Jerry starts his retirement account at age $47.$

$$ How much will be in the account when he retires? $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$$ How much of the final amount is money he put in$?\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$$ How much of the final amount is interest he earned? $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$$ What percent of the final amount is interest he earned? $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

c$)$ Mary starts her retirement account at age $37.$

$$ How much will be in the account when she retires? $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$$ How much of the final amount is money she put in$?\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$$ How much of the final amount is interest she earned? $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$$ What percent of the final amount is interest she earned? $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

d$)$ Cari starts her retirement account at age $27.$

$$ How much will be in the account when she retires? $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$$ How much of the final amount is money she put in$?\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$$ How much of the final amount is interest she earned? $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$$ What percent of the final amount is interest she earned? $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

e$)$ Review your answers to a$,$ b$,$ c and d to make sure you rounded dollar and percent figures correctly.

f$)$ Write a few sentences about the numbers and your observations on the answers to $1$a $1$d$.$ Say

something more sophisticated than, $$It$$s better to start early.$$

$2)$ Clarence, Kelly and Walter plan to retire at age $65.($Note it is not age $67$ like in question $1,$ so you

cannot use the same value of N that you used in question $1.)$ Each of them will contribute monthly to

an ordinary annuity paying $7\mathrm{.}2\%$ interest compounded monthly, and each of them wants to have

$$1,200,000$ in their account when they retire. Answer the following.

a$)$ Clarence starts his retirement account at age $45.$

i$.$ How much will Clarence need to contribute to the account each month in order to have

$$1,200,000$ in the account at age $65?$ Round UP to a whole$-$dollar amount.

ii$.$ Based on your rounded answer to a$)$ i$.,$ how much of the final balance of $$1,200,000$ will

Clarence contribute to the account? Round to nearest hundred dollars.

b$)$ Kelly starts her retirement account at age $35.$

i$.$ How much will Kelly need to contribute to the account each month in order to have

$$1,200,000$ in the account at age $65?$ Round UP to a whole$-$dollar amount.

ii$.$ Based on your rounded answer to b$)$ i$.$ how much of the final balance of $$1,200,000$ will Kelly

contribute to the account? Round to nearest hundred dollars.

c$)$ Walter starts his retirement account at age $25.$

i$.$ How much will Walter need to contribute to the account each month in order to have

$$1,200,000$ in the account at age $65?$ Round UP to a whole$-$dollar amount.

ii$.$ Based on your rounded answer to c$)$ i$.,$ how much of the final balance of $$1,200,000$ will

Walter contribute to the account? Round to nearest hundred dollars.

d$)$ Write a few sentences about the numbers and your observations on the answers to $2$a$,$ b$,$ c$.$ Say

something more sophisticated than, $$It$$s better to start early