Answer:
Explanation:
Q1 .
Money saved every month = $200
Time period until you retire = 35 years
Rate of Interest = 8%
The money is compounded monthly.
a). Amount for retirement = Saving annuity
Saving or making a series of payments at regular intervals is called annuity.
Annuity formula is :
P_{n} = d((1 + r/k)^{nk} - 1)/(r/k)
PN is the balance in the account after N years.
d is the regular deposit (the amount you deposit each month)
r is the annual interest rate in decimal form(R/100)
k is the number of compounding periods in one year
Here d= $200 , r = 0.08 , n = 35 years , k = 12 (compounded monthly)
P_{n} = 200((1 + 0.08/12)^{(35*12)} - 1)/(0.08/12)
= $ 458776.50
b). Looking at the formula used in above option we can -
Increase number of years to increase retirement amount
Increase the monthly amount deposited
Increasing rate of interest also increases the amount
Compounding Annually , half yearly or quaterly will decrease the amount
c). Let us change the amount from $200 to $300 . Then amount will be
P_{n} = d((1 + r/k)^{nk} - 1)/(r/k)
P_{n} = 300((1 + 0.08/12)^{(35*12)} - 1)/(0.08/12)
= $ 688164.75