Answer to Question #70499 in Finance for Nick Mango

Question

Today is his 24th birthday. He plans to retire at 65 years old and he expects to live for another 20 years afterwards. He wants an income of $30,000 per year during his retirement years, to be paid annually on his birthday (starting from his 65th birthday). He plans to save some amount at each birthday from the age 25 to 64. He thinks about saving a constant amount for the first 10 years and then increases his saving at 3% each year until the last one before his retirement. The bank provides two types of accounts. One account pays 6.9%/year compounded quarterly. The other account pays 7%/year compounded annually?
(a) Which account would you recommend? Why?
(b) After choosing the proper account, how much should your brother save each year
for the first 10 years?
(c) What is the balance of your brother’s account right after he makes his deposit in
his saving account on his 50th birthday?

Answer 1

a) I recommend 6.9%/year compounded quarterly, because if we calculate effective annual rate, we get 7,08%, that is more than account 7%/year compounded annually.
b) For the first 10 years your brother have such savings, as
Savings for 10 years = amount of savings(firstly)*(1+i/4)4*10.
c) balance of your brother's account = amount of savings(firstly)*(1+i/4)4*10 + [1,03*amount of savings(firstly)*(1+i/4)4]40.