For a loan with a fixed principal and interest rate, what is the effect of increasing the number of payments (n) on the monthly payment (P)?

The monthly payment stays the same.

The effect cannot be determined.

Which expression correctly calculates the monthly payment for a $15,000 car loan at 4.8% annual interest for 5 years (60 months)?

$\frac{15000 \cdot 0.048}{1 - (1.048)^{-60}}$

$\frac{15000 \cdot 0.004}{1 - (1.004)^{-60}}$

$\frac{15000 \cdot 0.004}{1 - (1.004)^{-5}}$

$\frac{15000 \cdot 0.048}{1 - (1.048)^{-5}}$

Geometric Sequences and Series Practice — Grade 11 math

Lesson 7: Geometric Sequences and Series — Practice Questions

1. Calculate the monthly payment for a $8,000 loan at 12% annual interest over 36 months. Round to the nearest cent. The monthly payment is ___ dollars.
2. For a loan with a fixed principal and interest rate, what is the effect of increasing the number of payments (n) on the monthly payment (P)?
- A. The monthly payment increases.
- B. The monthly payment decreases.
- C. The monthly payment stays the same.
- D. The effect cannot be determined.
3. A family takes out a $300,000 mortgage at 3.6% annual interest for 30 years. Calculate the monthly payment, rounded to the nearest cent. The payment is ___ dollars.
4. Which expression correctly calculates the monthly payment for a $15,000 car loan at 4.8% annual interest for 5 years (60 months)?
- A. $\frac{15000 \cdot 0.048}{1 - (1.048)^{-60}}$
- B. $\frac{15000 \cdot 0.004}{1 - (1.004)^{-60}}$
- C. $\frac{15000 \cdot 0.004}{1 - (1.004)^{-5}}$
- D. $\frac{15000 \cdot 0.048}{1 - (1.048)^{-5}}$
5. A person can afford monthly payments of $400 for a 4-year loan at 6% annual interest. What is the maximum loan principal they can afford, rounded to the nearest dollar? ___ dollars.
6. An annuity consists of monthly payments of $100 for 5 years at an annual interest rate of 6% compounded monthly. What is the total number of payments, represented by `nt` in the formula? ___
7. In the annuity formula, if the annual interest rate is `r` and payments are made `n` times per year, which expression represents the interest rate per compounding period?
- A. $r$
- B. $nt$
- C. $\frac{r}{n}$
- D. $\left(1 + \frac{r}{n}\right)$
8. For an annuity with quarterly payments at an 8% annual interest rate, what is the value of the denominator, $\frac{r}{n}$, in the future value formula? ___
9. David makes annual payments of $2000 into an annuity for 10 years at 5% interest compounded annually. Which expression correctly sets up the future value calculation?
- A. $\frac{2000 \left( \left(1 + 0.05\right)^{10} - 1 \right)}{0.05}$
- B. $\frac{2000 \left( \left(1 + \frac{0.05}{12}\right)^{10} - 1 \right)}{\frac{0.05}{12}}$
- C. $\frac{2000 \left( \left(1 + 0.05\right)^{120} - 1 \right)}{0.05}$
- D. $\frac{5000 \left( \left(1 + 0.10\right)^{10} - 1 \right)}{0.10}$
10. An annuity involves payments into an account with a 12% annual interest rate, compounded monthly. What is the value of the growth factor for each period, `(1 + r/n)`? ___