Question

A Asset Valuation = Price B Wealth Accumulation C Funding – Lump sum funds lump sum D Funding – Lump sum funds ordinary level annuity E Funding – Lump sum funds delayed level annuity F Funding – Ordinary level annuity funds lump sum G Funding – Ordinary level annuity funds delayed level annuity H Choosing Among Alternatives Classify the problem as one of the above types. Choose Only One You have purchased solar panels for your house and they will be installed in 10 months. You will pay $25,000 for the panels in 10 months. How much must you save (invest) each month, starting next month, for six months, to pay for the panels if your investments earn 3% APR, compounded monthly?

Answer 1

Future value of amount required = $25000 in 10 months

t=0 be this month. the panels must be paid for in 10 months including this month. hence $25000 must bepaid in t9

savings start from next month t1 and goes on till t7 (period of 6 months)

Annual rate =3%. hence monthly rate = 3/12 %.

At t=7, the $25000 would be worth = 25000/(1+0.0025)^2 = $24875.46

(Discounting the amount at t9 to find what it is worth at t7). In other words we would need $24875.46 in our hand at the end of 8th month (t7) to be able to pay $25000 at 10th month.

savings happen across 6 months. This can be considered as an annuity paid at the end of month or annuity due paid at the beginning of eachmonth.

Here let us consider we are saving a certain amount at the end of each month. We should have saved $24875.46 in these 6 months for us to be able to pay for the panel.

Using future value formula,

Let amount to be saved each year be P

24875.46 = P((1+0.0025)^6-1)/0.0025)

Solving the equation we get $4120.07. Hene we should save $4120.46from next month for a period of six months to be able to pay for the panel.