Instructions: Show your steps clearly. Write your justification as to why you wi
ID: 2912822 • Letter: I
Question
Instructions: Show your steps clearly. Write your justification as to why you will be using the formulas in each step. 1. Dan Hook deposits $400 a month to a retirement account that has interest rate of 3.1%, compounded monthly. After making 60 deposits, Dan changes his job and stops making payments for 3 years. After 3 years, he starts making deposits again, but now he deposits $525 monthly. What will the total value of the retirement accounts be a. After Dan makes his $400 monthly deposit for five years? b. Eight years after his first deposit of $400? c. After Dan makes his $525 monthly deposits for 5 years?Explanation / Answer
The formula for annual compound interest, including principal sum, is:
A = PMT * (((1 + r/n)^nt - 1) / (r/n)) * (1+r/n)
Where:
A = The future value of the Deposit, including interest
P = the principal Deposit amount
PMT = the monthly payment
r = the annual interest rate
n = the number of times that interest is compounded per year (i.e Monthly)
t = the number of years the money is invested or borrowed for
A = [ $400 * (((1 + 0.031/12)60 - 1) / (0.031/12)) ]
A = $25,990.78
After stop making payment
A = P(1+r/n)(nt)
A = $25990.78 * ( 1+.031/12) (12*3)
A = $28520.47
After 3 years, A :
A = [ Compound interest for principal ] + [ Future value of a series ]
A = [ P(1+r/n)^(nt) ] + [ PMT * (((1 + r/n)^nt - 1) / (r/n)) ]
A = $28520.47 *( 1+.031/12) (12*5) + [ $525 * (((1 + 0.031/12)60 - 1) / (0.031/12)) ]
A = $ 67,408.40
The value of the retirement account after Dan makes his $525 monthly deposits for 5 years would be $ 67,408.40.