Question

If you want to have $87654 in the bank at the end of 10 years and you get a 3% interest rate per year. How much money do you need to deposit each month if a) monthly compounding? b) semi-annual compounding? a quarterly compounding? d) daily compounding?

Answer 1

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