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Bo decides to establish a fund that it will use 10 years from now to replace an aging production facility. The company will make a $100,000 initial contribution to the fund and plans to make quarterly contributions of $50,000 beginning in three months. The fund earns 12%, compounded quarterly. What will be the value of the fund 10 years from now

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Answer: $4,096,266.76

Explanation:

First find the value of the initial $100,000 ten years into the future.

Rate = 12% / 4 = 3% quarterly

Period = 10 * 4 = 40 quarterly periods

= 100,000 * (1 + 3%)⁴⁰

= $326,203.78

This will be added to the future value of the $50,000 annuity.

Future value of annuity = Annity * ( ( 1 + rate)^number of periods - 1) / rate

= 50,000 * ( ( 1 + 3%) ⁴⁰ - 1) / 3%

= $3,770,062.99

Add both future values:

= 3,770,062.99 + 326,203.78

= $4,096,266.76

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