Question

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Suppose that $2000 is invested at a rate of 5.1%, compounded semiannually. Assuming that no withdrawals are made, find the total amount after 6 years.
Do not round any intermediate computations, and round your answer to the nearest cent.

Answer 1

The total amount after 6 years is $ 2705.5649

Solution:

The formula for compound interest, including principal sum, is:

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

Where,

A = the future value of the investment/loan

P = the principal investment amount

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per unit t

t = the time the money is invested

From given,

p = 2000

$r = 5.1 \% = \frac{5.1}{100} = 0.051$

t = 6 years

n = 2 (  compounded semiannually)

Substituting the values we get,

$A = 2000( 1 + \frac{0.051}{2})^{ 2 \times 6}\\\\A = 2000( 1 + 0.0255)^{12}\\\\\A = 2000(1.0255)^{12}\\\\A = 2000 \times 1.35278\\\\A = 2705.5649$

Thus the total amount after 6 years is $ 2705.5649