Question

If you invest $8,700 per period for the following number of periods, how much would you have: Use Appendix C for an approximate answer, but calculate your final answer using the formula and financial calculator methods.

a.	In 14 years at 7 percent? (Do not round intermediate calculations. Round your final answer to 2 decimal places.) b. In 25 years at 7 percent? (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

Answer 1

a) If you invest $8700 per year for 14 years at 7%, you will have:

Since the cash invested per year is same, we can also add up the compounding factor and the multiply it with the sum invested.

= 8700[(1+0.07)¹+(1+0.07)²+(1+0.07)³+(1+0.07)⁴+(1+0.07)⁵+(1+0.07)⁶+(1+0.07)⁷+ (1+0.07)⁸+ (1+0.07)⁹+(1+0.07)¹⁰+(1+0.07)¹¹+(1+0.07)¹²+(1+0.07)¹³+(1+0.07)¹+(1+0.07)¹⁴]

= 8700 [ 1.07+1.1449+1.225+1.31+1.42+1.50+1.60+1.71+1.83+1.96+2.10+2.25+2.41+2.58]

= 8700 ( 24.12 ) = $209830.38 approx.

b) If you invest $8700 per year for 25 years at 7%:

Future value= 8700[(1+0.07)¹+(1+0.07)²+(1+0.07)³+(1+0.07)⁴+(1+0.07)⁵+(1+0.07)⁶+(1+0.07)⁷+ (1+0.07)⁸+ (1+0.07)⁹+(1+0.07)¹⁰+(1+0.07)¹¹+(1+0.07)¹²+(1+0.07)¹³+(1+0.07)¹⁴+(1+0.07)¹⁵+ (1+0.07)¹⁶+(1+0.07)¹⁷+(1+0.07)¹⁸+(1+0.07)¹⁹+(1+0.07)²⁰+(1+0.07)²¹+(1+0.07)²²+(1+0.07)²³+ (1+0.07)²⁴+(1+0.07)²⁵]

=8700[1.07+1.1449+1.225+1.31+1.42+1.50+1.60+1.71+1.83+1.96+2.10+2.25+2.41+2.58+2.76+ 2.95+3.16+ 3.38+3.62+3.87+4.14+4.43+4.74+5.07+5.42]

= 8700 ( 67.65) = $588554.13 approx