Question

Assume you will invest $100 per month in an investment earning 11% per year (assume monthly compounding). After 10 years, you stop making the monthly payment. The money you have accumulated after 10 years remains invested and continues to earn 11% (compounded annually) for an additional 20 years (with no further payments made). How much do you have at the end of the total 30 year period?

Answer 1

Answer:

The amount at the end of 30 years is $174,952.

Explanation:

In this problem we first need to determine the future value after making A = $100 investment for n = 10 years at r = 11% per year compounded monthly.

Then we need to compute the compound interest on this future value for 20 years at 11% interest compounded annually.

The future value formula is:

$FV=A\times [\frac{(1+r)^{n}-1}{r}]$

The amount is compounded monthly.

The rate of interest per month is:

$r=\frac{11}{12}\%= 0.9167\%$

The number of periods is: n = 10 × 12 = 120 months.

Determine the future value as follows:

$FV=100\times [\frac{(1+0.009167)^{120}-1}{0.009167}]=21700$

Thus, the amount at the end of 10 years is $21700.

Now this amount is kept the account for t = 20 years and earns an interest at the rate of 11% compounded annually.

Amount at the end of 30 years = $FV(1+r)^{t}$

                                                    $=21700\times(1+0.11)^{20}\\=174952$

Thus, the amount at the end of 30 years is $174,952.

Answer 2

Answer:

$174,950.7

Explanation:

Given:

Monthly payment(C) = $100

Rate (I) = 11% yearly = 11/12 = 0.916667% monthly = 0.00916667

number of annuity = 10 x 12 = 120

Calculation:

$Future\ investment = C[\frac{(1+I)^N-1}{I} ]\\=100[\frac{\ (1+0.00916667)^{120}-1}{0.00916667} ]\\=100[\frac{(1.00916667)^{120}-1}{0.00916667} ]\\=100[\frac{2.98915079-1}{0.00916667} ]\\=100[\frac{1.98915079\\}{0.00916667} ]\\=100[216.998189]\\=21699.8189$

 Reinvest $21699.8189, when n=20 r= 11%

$A = P(1+r)^n\\=21699.8189(1+.11)^{20\\}\\=21699.8189(1.11)^{20}\\=21699.8189(8.06231154)\\=174,950.7$

Total Amount he get is $174,950.7