Question

Parents of a student are saving money for his study cost of $40,000 to be needed at the end of 5 years from now. The parents have decided to deposit $6,000 at the end of each year into a bank account that pays interest at 16% compounding quarterly. If there is no withdrawal, find

1. the amount of money the parents will get from this bank account at the end of 5 years =  
2. the effective annual rate =  

Answer 1

b)

first lets calculate effective annual interest rate (EAR)

EAR = (1 + r/n)^n - 1

where r = yearly interest = 16%

n = compounding periods (here it is given quarterly compounding so n = 4)

EAR = (1 + 0.16/4)^4 - 1

= 16.986%

a)

amount after 5 years can be found using the future value of annuiyt formula

future value of annuity = PMT[ (1+r)^n - 1 / r ]

where PMT = yearly deposits = $6000

n = number of years = 5

r = EAR = 16.986%

amount at the end of 5 years( future value) = 6000 [ (1+ 0.16986)^5 - 1 / 0.16986 ]

= $42,074.65(rounded to nearest cent)