Question

Leon Bogut just received a signing bonus of $916,300. His plan is to invest this payment in a fund that will earn 10%, compounded annually.

a) If Bogut plans to establish the AB Foundation once the fund grows to $2,875,743, how many years until he can establish the foundation?

b) Instead of investing the entire $916,300, Bogut invests $278,700 today and plans to make 12 equal annual investments into the fund beginning one year from today. What amount should the payments be if Bogut plans to establish the $2,875,743 foundation at the end of 12 years?

Answer 1

a.We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

2,875,743=916300*(1.1)^n

(2,875,743/916300)=(1.1)^n

Taking log on both sides;

log(2,875,743/916300)=n*log 1.1

n=log(2,875,743/916300)/log 1.1

=12 years

b.

We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

Future value of 278700=278700*(1.1)^12

Also:

Future value of annuity=Annuity[(1+rate)^time period-1]/rate

=Annuity[(1.1)^12-1]/0.1

Hence

2,875,743=278700*(1.1)^12+Annuity[(1.1)^12-1]/0.1

2,875,743-874,679.9886=Annuity[(1.1)^12-1]/0.1

Annuity[(1.1)^12-1]/0.1=2,001,063.011

Annuity*21.38428377=2,001,063.011

Annuity=2,001,063.011/21.38428377

=$93576.34(Approx).