Question

You want to save (deposit) $7340 per year, starting next year, to make a down payment of $83384 on a vacation home. If you can earn 4.73 percent on your investment, for how many years will you have to make deposits?

Answer 1

Future Value of Annuity = Present Value *[( 1+ rate of Interest) ^ Time -1 ] Rate of Interest

$ 83,384 = $ 7,340 * [( 1+4.73%) ^ Time-1] / 4.73%

or $ 83,384 = 155,179.704 *[( 1+4.73%) ^ Time-1]

or $ 83,384 / 155,179.704 =[( 1+4.73%) ^ Time-1]

or 0.53733831 = [( 1.0473) ^ Time-1]

or 1.53733831 = ( 1.0473) ^ Time

Let Time be n years

Taking log on both sides,

log 1.53733831 = n log (1.0473)

n = log 1.53733831 / log (1.0473)

= 9.305390184

= 9.31 Years

Hence the correct answer is 9.31 Years