Answer:
Target Amount T=$87654
Number of Years =10 years
Annual rate R=3%
Let A be the monthly amount
1)
if Monthly compounding
N=10*12=120 Months
r=R/12=3%/12=0.25%
So A= T*r/((1+r)^N-1)
A=85674*0.25%/((1+0.25%)^120-1)
A=$613.09
2) if Semi compounding
Then Effective annual rate Rf=(1+R/2)^2-1=(1+3%/2)^2-1=3.0225%
N=10*12=120 Months
r=Rf/12=3.0225%/12=0.2519%
So A= T*r/((1+r)^N-1)
A=85674*0.2519%/((1+0.2519%)^120-1)
A=$612.37
3)
if quarterly compounding
Then Effective annual rate Rf=(1+R/4)^4-1=(1+3%/4)^4-1=3.0339%
N=10*12=120 Months
r=Rf/12=3.0339%/12=0.2528%
So A= T*r/((1+r)^N-1)
A=85674*0.2528%/((1+0.2528%)^120-1)
A=$612.01
4)
if Daily compounding
Then Effective annual rate Rf=(1+R/365)^365-1=(1+3%/365)^365-1=3.0453%
N=10*12=120 Months
r=Rf/12=3.0453%/12=0.2538%
So A= T*r/((1+r)^N-1)
A=85674*0.2538%/((1+0.2538%)^120-1)
A=$611.65
If you want to have $87654 in the bank at the end of 10 years and...
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