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?

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:

The amount is compounded monthly.

The rate of interest per month is:

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

Determine the future value as follows:

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 =

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

$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:

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

Total Amount he get is $174,950.7

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