A = P * [1 + (r/n)]^(n*t)

Where:

A = Amount

P = Principle (amount deposited)

r = annual interest rate

n = number of times compounded in one year

t = number of years

Let’s plug in those values:

A = P * [1 + (r/n)]^(n*t)

A = $2500 * [1 + (.055/4)]^(4*4)

A = $2500 * [1 + (0.01375)]^(16)

A = $2500 * [1.0375]^(16)

A = $2500 * 1.2442105384947

A = $3110.53

Rounded to the nearest dollar = $3110

Good luck in your studies,

~ Mitch ~

P.S. – Sarah’s equation is way off base.

We can make a rough estimate the final answer:

$2500.00 * 5.5% = $137.50 <-- First Year $2637.50 * 5.5% = $145.06 <-- Second Year $2782.56 * 5.5% = $153.04 <-- Third Year $2935.60* 5.5% = $161.46 <-- Fourth Year $2935.60 + $161.46 = $3907.06 There's no way it could be $5888!

P is your initial investment, or 2500.

R is the rate (written as a decimal), so 5.5% = .055

N is the time period in which the money compounds (quaterly = 4, yearly = 12, etc.) so here, N is 4.

T is time. 4 years, so 4.

Substitute.

A = 2500(1 + .055/4)^(4 x 4)

Solve.

2500(1.01375)^16

2500(1.244210538)

A = 3110.526346 = $3,110.53

Well, we got different answers. I’ve always used this equation. The only difference is they used “i” (same as my R), but I divided by N, the incriments when the money compounds.

The above calculates the future value, (FV), of an investment, (PV), accruing at a fixed interest rate of i% for n periods.

each year has 4 quarters for 4 yrs 4 *4 =16 = n

FV = 2500(1+.055)^16 = $5888

Sorry they are right. I used the right equation but forgot to divide the interest rate over the 4 quarters.