Q: Which formula should be used to calculate the amount $$A$$ after $$t$$ years for a principal $$P$$ invested at an annual interest rate $$r$$ compounded $$n$$ times per year?

$$A = P \times \left(1 + \frac{r}{n}\$$right)^{nt}$$

Q: What is the present value formula for an amount $$A to be $$received after $$t$$ years, assuming a per annum interest $$r$$ compounded $$n$$ times per year?

$$P = A \times \left(1 + \frac{r}{n}\$$right)^{-nt}$$

Question 1

A principal of $2000 is invested at an annual interest rate of 1.5% compounded quarterly. What is the amount in the account after 1 year?

Accepted Answer

$2030.17

Question 2

Which formula should be used to calculate the amount $$A$$ after $$t$$ years for a principal $$P$$ invested at an annual interest rate $$r$$ compounded $$n$$ times per year?

Accepted Answer

$$A = P 	imes \left(1 + \frac{r}{n}\$$right)^{nt}$$

Question 3

If $$300 is $$invested at $$6\%$$ compounded daily for $$4$$ years, what is the resulting amount?

Accepted Answer

$$381.37$$

Question 4

What happens to the amount after 1 year if the number of times that the interest is compounded is increased without bound?

Accepted Answer

The amount approaches the value given by continuous compounding

Question 5

Which formula is used for continuous compounding?

Accepted Answer

$$A = P 	imes e$$^{rt}$$

Question 6

Kameren invests $$6000 at$$ $$10\%$$ compounded semiannually for $$20$$ years. Obed invests $$6000 at$$ $$9.7\%$$ compounded continuously for $$20$$ years. Who has more money after $$20$$ years?

Accepted Answer

Kameren

Question 7

What is the present value formula for an amount $$A to be $$received after $$t$$ years, assuming a per annum interest $$r$$ compounded $$n$$ times per year?

Accepted Answer

$$P = A 	imes \left(1 + \frac{r}{n}\$$right)^{-nt}$$

Question 8

How much should you invest now to receive $$1000$$ after $$10$$ years at $$7\%$$ compounded monthly?

Accepted Answer

$$497.60$$

Question 9

How much should you invest now to receive $$1000$$ after $$10$$ years at $$6\%$$ compounded continuously?

Accepted Answer

$$548.81$$

Question 10

What rate of interest compounded annually is needed to double an investment in $$7$$ years?

Accepted Answer

$$10.41\%$$

Question 11

How long will it take for an investment to double in value if it earns $$6\%$$ compounded quarterly?

Accepted Answer

$$11.64$$ years

Question 12

How long will it take for an investment to double in value if it earns $$6\%$$ compounded continuously?

Accepted Answer

$$11.55$$ years

Question 13

How long will it take for an investment to triple in value if it earns $$6\%$$ compounded continuously?

Accepted Answer

$$18.3$$ years

Question 14

If the present value of $$A$$ dollars to be received after $$t$$ years with continuous compounding is $$P$$, which formula is correct?

Accepted Answer

$$P = Ae$$^{-rt}$$

Question 15

Which of the following best describes compound interest?

Accepted Answer

Interest paid on the principal and previously earned interest

Question 16

A principal of $$P$$ dollars is borrowed for $$t$$ years at a per annum interest rate $$r. $$What is the simple interest formula?

Accepted Answer

$$I = P 	imes r 	imes t$$

Question 17

If you want to compare two investments, one compounded semiannually and one compounded continuously, which will generally yield more after a long period?

Accepted Answer

The one compounded continuously

Question 18

If you invest $$2000 at$$ $$8\%$$ compounded daily for $$1$$ year, what is the amount after $$1$$ year?

Accepted Answer

$$2166.56$$

Question 19

What is the definition of principal in financial mathematics?

Accepted Answer

The total amount borrowed or invested

Question 20

Which payment period corresponds to compounding 12 times per year?

Accepted Answer

Monthly

Precalculus Financial Models: Compound Interest, Doubling/Tripling Time, and Interest Rate Problems

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