Question

You expect that you will need to replace your furnace in 5 years at a cost of $16,447. How much must you save, each month for 14 months, starting next month (the same amount each month) if your savings account pays 2.27% APR (compounded monthly)?

Answer 1

QUESTION SUMMARY : To calculate monthly savings for 14 months at 2.27 APR to replace furnace in 5 years

Answer : 1146.6 $

There are 2 parts to this investment

1. annuity of Y $ for 14 months (= 1.1667 years) which totals to say X and

2. X invested for next 46 months (= 3.8333 years)

Amount after these 46 months (= 3.8333 years) will be 16447 n= 12 as it is compounded monthly

so X is the PV +   FV / ( 1+ r/n) ^n *t

= 16447____________________

(1 + 0.0227/12 )^ 12* 3.8333

= 16447 / 1.0908

= 15077.92 $

X is the future value of an annuity of Y $

so finding Y with the formula :

Assumption : It is a ordinary annuity

Future value X = Annuity of $ Y * [(1+i/n)^ nt −1]

i / n

Y = 1146.6 $