Two partners agree to invest equal amounts in their business. One will contribute $10,000 immediately. The other plans to contribute an equivalent amount in 3 years, when she expects to acquire a large sum of money. How much should she contribute at that time to match her partner's investment now, assuming an interest rate of 6% compounded semiannually?

Answer: $11,940.5

Step-by-step explanation:

The standard formula for compound interest is given as;

A = P (1+r/n) ^ (nt) ... 1

Where;

A = final amount/value

P = initial amount/value (principal)

r = rate yearly

n = number of times compounded yearly.

t = time of investment in years

For this case;

Since we want to determine the value that will be equivalent to $10,000 in 3years.

P = $10,000

t = 3years

n = 2 (semiannually)

r = 6% = 0.06

Using equation 1.

A = 10,000 (1+0.06/2) ^ (2*3)

A = 10,000 (1.03) ^6

A = 10,000 (1.194052296529)

A = $11,940.5