Question

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

Answer 1

A = $41,867.06

A = P + I where

P (principal) = $14,000.00

I (interest) = $27,867.06

Explanation:

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

To find: The accumulated value of an investment

Formula:
`A = P(1 + (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.

Answer 2

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+(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+(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.