Question

Your mother has asked for your help. She would like to save up $30,000 to take your family on a trip in 3 years. She wants to make monthly deposits into an account that she thinks will pay 6%. How much must she invest each month to reach her goal

Answer 1

Answer:

The answer to the question is

She must invest $251.85 each month to reach her goal

Step-by-step explanation:

Future value of an annuity is the amount a given stream of cash flows will be worth after a specified period. The future value represents the cumulative accumulation of payments made or borrowed and their respective interest made or interest charged.

The future value is given by

$FV = PMT\frac{(1+r)^{n}-1 }{r}$

Where

FV = Future value =$30,000

PMT = Payment =

r = Interest rate for a given period = 6 % monthly

n = Number of periods of payments = 3 years or 36 months

Therefore we have

$30000=PMT\frac{(1+0.06)^{36} -1}{(0.06)}$  = PMT×119.12

Therefore PMT = 30000÷119.12 = $251.85

Therefore She would have to save $251.85 monthly to make up $30,000 in three years

Answer 2

Answer:

$50 per month

Step-by-step explanation:

Given

Total amount needed=$30,000

Deposits 3 years= 36 months

6% of the total amount

=6/100×$30,000

= 0.06×$30,000

=$1,800

She wants to make deposits if $1,800 over a period of 36 months

=$1,800/36

=$50 per month