Question

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 2 years. How much should she contribute at that time to match her​ partner's investment​ now, assuming an interest rate of 9​% compounded quarterly​?

Answer 1

Answer:

She should contribute $ 8369.38 ( approx )

Step-by-step explanation:

Let P be the amount invested by the other partner,

∵ The amount formula in compound interest,

$A=P(1+\frac{r}{n})^{nt}$

Where,

r = annual rate,

n = number of compounding periods in a year,

t = number of years,

Here, r = 9% = 0.09, n = 4 ( quarters in a year ), t = 2 years,

Then the amount after 2 years,

$A = P(1+\frac{0.09}{4})^{8}$

According to the question,

A = $ 10,000,

$P(1+\frac{0.09}{4})^{8}= 10000$

$P(1+0.0225)^8 = 10000$

$\implies P = \frac{10000}{1.0225^8}\approx \ 8369.38$