Question

Bernadette needs to make some house repairs in three years that will cost $8,000. She has some money in an account earning 6% annual interest. How much money needs to be in the account today so she will have enough to pay for the repairs? $6,717 $5,978 $6,950 O $5,880 $6,376 Unfortunately, Bernadette doesn't have enough money in her account right now. She needs to make additional contributions at the end of each of the next three years to be able to pay for the repairs. Her account currently has $3,500, which, along with her additional contributions, is expected to continue earning 6% annual interest. If she makes equal contributions each year, how large must each contribution be for Bernadette to have $8,000 after three years? $445 O $770 O $1,203 O 9417 $562

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.

8000=P*(1.06)^3

P=8000/(1.06)^3

=$6717(Approx).

2.A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

Future value of 3500=3500*(1.06)^3

=4168.556

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

=Annuity[(1.06)^3-1]/0.06

Hence

8000=4168.556+Annuity[(1.06)^3-1]/0.06

8000=4168.556+Annuity*3.1836

Annuity =(8000-4168.556)/3.1836

=$1203(Approx).