Question

Find the accumulated value of an investment of $14,000 at 10% compounded semiannually for 11 year

Answer 1

Given:

Principal = $14000

Rate of interest = 10% compounded semiannually.

Time = 11 years.

To find:

The accumulated value of the given investment.

Solution:

Formula for amount or accumulated value after compound interest is:

$A=P\left(1+\dfrac{r}{n}\right)^{nt}$

Where, P is the principal values, r is the rate of interest in decimal, n is the number of times interest compounded in an year and t is the number of years.

Compounded semiannually means interest compounded 2 times in an years.

Putting $P=14000,r=0.10,n=2,t=11$ in the above formula, we get

$A=14000\left(1+\dfrac{0.10}{2}\right)^{2(11)}$

$A=14000\left(1+0.05\right)^{22}$

$A=14000\left(1.05\right)^{22}$

$A\approx 40953.65$

Therefore, the accumulated value of the given investment is $40953.65.

Answer 2

Answer:

A = $41,867.06

A = P + I where

P (principal) = $14,000.00

I (interest) = $27,867.06

Step-by-step explanation:

Given: Investment = $14,000 Annual Rate: 10% compounded semiannually = 11 year

To find: The accumulated value of an investment

Formula: $A = P(1 + \frac{r}{n}) ^n^t$

Solution: First, convert R as a percent to r as a decimal

r = R/100

r = 10/100

r = 0.1 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 14,000.00(1 + 0.1/12)(12)(11)

A = 14,000.00(1 + 0.008333333)(132)

A = $41,867.06

Henceforth:

The total amount accrued, principal plus interest, with compound interest on a principal of $14,000.00 at a rate of 10% per year compounded 12 times per year over 11 years is $41,867.06.