Question

1.) You are saving for clinic upgrades you would like to make 4 years from now. How much will you have to set aside at the end of each year to have $30,000 in 5 years if the interest rate is 7.25% compounded semiannually?

2.) A business manager deposits $2,000 in a savings account at the end of each year for five years, what will be the value of her investment at an annual rate of 6.25% with daily compounding?

please show your work out in excel

Answer 1

Ans 1.
Given interest rate APR =7.25% compounded semi annually
EAR =(1+7.25%/2)^2-1=7.3814% pa.
We need tyo find the periodic savings for the annuity
with FV of $30,000 after 5 years.
Formula for future value of Ordinary Annuity :
FV= A [ {(1+k)n-1}/k]
FV = Future annuity value=$30,000
A = periodical investment=??
K=interest rate=7.3814% pa
N=periods=5 years
30,000=A*[1.073814^5-1]/7.3814%
A= $5,177.18
So Annual savings amount is $5,177.18
Ans 2.
Interest rate is 6.25% ps compounded daily
EAR =(1+6.25%/365)^365-1=6.4489% pa
Formula for future value of Ordinary Annuity :
FV= A [ {(1+k)n-1}/k]
FV = Future annuity value=??
A = periodical investment=2000 per year
K=interest rate=6.4489%
N=periods=5 years
FV =2000*[1.064489^5-1]/6.4489%
FV =$11,375.67
So the Maturity value of the investment will be $11,375.67