Mr. Merkel has contributed ​$83.00 at the end of each six months into an RRSP paying 5 % per annum compounded annually. How much will Mr. Merkel have in the RRSP after 10 ​years?

To solve this problem, we will use the future value formula for an annuity, since Mr. Merkel is making regular contributions to his Registered Retirement Savings Plan (RRSP).

### Given information:
- Contribution amount per period ($PMT$) = $83
- Interest rate per annum ($r$) = 5% or 0.05
- Number of periods per year = 2 (since contributions are made semi-annually)
- Time in years ($t$) = 10 years
- Compounding frequency = annually (although contributions are semi-annual)

First, let's compute the interest rate per period and the total number of periods:
- The interest rate per period is $r_{per} = \frac{0.05}{2} = 0.025$ (since there are two periods in a year).
- The total number of periods over 10 years is $n = 10 \times 2 = 20$.

Now, we will use the future value formula for an ordinary annuity (since contributions are made at the end of each period):
\[
FV = PMT \times \frac{(1 + r_{per})^n - 1}{r_{per}}
\]
Where:
- $FV$ is the future value
- $PMT$ is the periodic payment ($83)
- $r_{per}$ is the interest rate per period (0.025)
- $n$ is the total number of periods (20)

### Calculation:
\[
FV = 83 \times \frac{(1 + 0.025)^{20} - 1}{0.025}
\]
\[
FV = 83 \times \frac{(1.025)^{20} - 1}{0.025}
\]
\[
FV = 83 \times \frac{1.638616439 - 1}{0.025}
\]
\[
FV = 83 \times \frac{0.638616439}{0.025}
\]
\[
FV = 83 \times 25.54465756
\]
\[
FV \approx 2110.20
\]

### Conclusion:
After 10 years, Mr. Merkel will have approximately **$2,110.20** in his RRSP.

Would you like more details on the calculation, or do you have any questions?

Here are some related questions to explore:
1. How does the compounding frequency affect the future value of investments?
2. What happens if contributions are made at the beginning of each period?
3. How would the future value change if the interest rate were 6% instead of 5%?
4. What would happen to the total amount if Mr. Merkel increased his contributions?
5. How does the length of time invested impact the growth of the RRSP?

**Tip**: The future value of an annuity increases more rapidly with longer investment periods due to the power of compounding interest.

Mr. Merkel has contributed ​$83.00 at the end of each six months into an RRSP paying 5% per annum compounded annually. How much will Mr. Merkel have in the RRSP after 10 ​years?

Discover how to calculate the future value of an annuity with regular semi-annual contributions. Using a $83 contribution at 5% annual interest, this solution walks through the steps to find how much Mr. Merkel will accumulate in his RRSP after 10 years.

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