You have decided to take a vacation to New Zealand in 8 years. You estimate the trip will cost $12,500. You currently have $1,800 in an account yielding 0.2% month. How much will you have to save each month to reach your goal? I got $147.65 a month. Is that correct
you will need a PV of 10700
x( 1 - 1.002^-96)/.002 = 10700
x(87.267434..) = 10700
x = 122.61
How did you get 147.65 ?
Under the function key of excel - the PMT key =PMT(0.2%/12,96,-1800,-12500)
PMT = ?
PV = $1,800
FV = $12,500
Rate = 0.2%/12
NPER = 96
$148.08
This what I got.
To determine how much you will need to save each month to reach your goal, we can use the concept of compound interest. Here's how to calculate it:
1. First, convert the interest rate to a monthly rate. Since the given interest rate is an annual rate, we need to divide it by 12 to get the monthly rate.
0.2% / 12 = 0.002 (0.2% is equivalent to 0.002 as a decimal)
2. Next, calculate the future value (FV) of your current savings and the monthly deposits over the 8-year period. We'll assume monthly contributions.
FV = P * (1 + r)^n - 1 / r
Where:
- P is the monthly deposit
- r is the monthly interest rate
- n is the number of periods (months)
In this case:
P = unknown
r = 0.002 (monthly interest rate)
n = 8 years * 12 months/year = 96 months
FV = $12,500 (the desired future value)
3. Rearrange the formula to solve for P:
P = (FV * r) / ((1 + r)^n - 1)
Plugging in the values:
P = ($12,500 * 0.002) / ((1 + 0.002)^96 - 1)
Now we can calculate the value of P to determine how much you need to save each month:
P = ($12,500 * 0.002) / ((1.002)^96 - 1)
P ≈ $147.65
So, based on the calculations, you are correct. You will need to save approximately $147.65 per month to reach your goal of $12,500 in 8 years, considering the given interest rate and current savings.