In: Finance
Signs (PV) | |||||||
1. You want to have this amount at the end | 913 | ||||||
Your money will be invested this number of years | 14 | ||||||
You will invest this amount each year | 29 | ||||||
The rate you will earn each year is this | 4.6% | ||||||
How much should you start your investment with, today? | |||||||
A Between 50.00 and 200.00 | |||||||
B Between 200.00 and 250.00 | |||||||
C Between 250.00 and 300.00 | |||||||
D Between 300.00 and 500.00 |
Future value of annuity=Annuity[(1+rate)^time period-1]/rate
=29[(1.046)^14-1]/0.046
=29*19.0632736
=552.834934
We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.
Hence A=deposit at beginning*(1.046)^14
Required future value=Future value of annuity+Deposit at beginning*(1.046)^14
913=552.834934+Deposit at beginning*(1.046)^14
Deposit at beginning=(913-552.834934)/(1.046)^14
=$191.89(Approx)
Hence the correct option is:
Between 50.00 and 200.00