Boyce invested an average of $450 per month since age 34 in various securities for his retirement savings. His investments averaged a 4% annual rate of return until he retired at age 63. Given the same monthly investment and rate of return, how much more would Boyce have in his retirement savings had he started investing at age 20? Assume monthly compounding.

a $113,320. 00

b $321,946. 93

c $78,624. 00

d $224,749. 27

If Boyce had started investing when he was 20 the amount he would have more than he does in his retirement savings would be b. $321,946.93.

How much more would Boyce have?

First convert the interest to a monthly rate:

= 4% / 12 months

= 1 / 3 %

Period:

= (63 - 34) x 12 months a year

= 348 months

Amount saved:

= Amount x ( (1 + rate) ^ number of periods - 1) / rate

= 450 x ( (1 + 1/3%)³⁴⁸ - 1 ) / 1/3%

= $294,811.07

If he started saving at 20, the number of periods would be:

= (63 - 20) x 12

= 516 months

Amount saved:
= 450 x ( (1 + 1/3%)⁵¹⁶ - 1 ) / 1/3%

= $616,758

The difference is:

= 616,758 - 294,811.07

= $321,946.93

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