In: Finance

# Calculate the amount of money that will be in each of the following accounts at the end of the given deposit period:

(Compound interest with non-annual periods) Calculate the amount of money that will be in each of the following accounts at the end of the given deposit period:

 Account Holder Amount Deposited Annual Interest Rate Compounding Periods per Year (M) Compounding Periods (Years) Theodore Logan TIT \$ 1,000 10% 1 10 Vernell Coles 95,000 12 12 1 Tina Elliott 8,000 12 6 2 Wayne Robinson 120,000 8 4 2 Eunice Chung 30,000 10 2 4 Kelly Cravens 15,000 12 3 3

## Solutions

##### Expert Solution

Given data:

Account Holder: Theodore Logan III

Principal Amount $$P=\ 1,000$$

Rate of Interest $$r=10 \%$$

Compounding Period per year $$m=1$$ (number of years compounding)

Period of deposit $$n=10$$ years

Step 1:

Let us assume that the amount to be received by Theodore Logan III is $$A$$.

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

$$A=1,000\left(1+\frac{0.10}{1}\right)^{10 \times 1}$$

$$A=1,000(1.10)^{10}$$

$$A=1,000(2.594)$$

$$A=\ 2,594$$

Account Holder: Vernell Coles

Principal Amount $$P=\ 95,000$$

Rate of Interest $$r=12 \%$$

Compounding Period per year $$m=12$$ (number of years compounding)

Period of deposit $$n=1$$ year

Step 1 :

Let us assume that the amount to be received by Vernell Coles is $$A$$.

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

$$A=95,000\left(1+\frac{0.12}{12}\right)^{1 \times 12}$$

$$A=95,000(1+0.01)^{12}$$

$$A=95,000(1.01)^{12}$$

$$A=95,000(1.127)$$

$$A=\ 1,07,065$$

Given data:

Account Holder: Tina Elliott

Principal Amount $$P=\ 8,000$$

Rate of Interest $$r=12 \%$$

Compounding Period per year $$m=6$$ (number of years compounding)

Period of deposit $$n=2$$ years

Step 1:

Let us assume that the amount to be received by Tina Elliott is $$A$$.

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

$$A=8,000\left(1+\frac{0.12}{6}\right)^{2 \times 6}$$

$$A=8,000(1+0.02)^{12}$$

$$A=8,000(1.02)^{12}$$

$$A=8,000(1.268)$$

$$A=\ 10,144$$

Account Holder: Wayne Robinson

Principal Amount $$=\ 120,000$$

Rate of Interest $$=8 \%$$

Compounding Period per year $$m=4$$

Period of deposit $$\mathrm{n}=2$$ years

Step 1 :

Let us assume that the amount to be received by Wayne Robinson is A.

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

$$A=120,000\left(1+\frac{0.08}{4}\right)^{2 \times 4}$$

$$A=120,000(1+0.02)^{8}$$

$$A=120,000(1.02)^{8}$$

$$A=120,000(1.1720)$$

$$A=\ 1,40,640$$

Account Holder: Eunice Chung

Principal Amount $$=\ 30,000$$

Rate of Interest $$=10 \%$$

Compounding Period per year $$m=2$$

Period of deposit $$\mathrm{n}=4$$ years

Step 1

Let us assume that the amount to be received by Eunice Chung is A.

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

$$A=30,000\left(1+\frac{0.10}{2}\right)^{4 \times 2}$$

$$A=30,000(1+0.05)^{8}$$

$$A=30,000(1.05)^{8}$$

$$A=30,000(1.4770)$$

$$A=\ 44,310$$

Account Holder: Kelly Cravens

Principal Amount $$=\ 15,000$$

Rate of Interest $$=12 \%$$

Compounding Period per year $$m=3$$

Period of deposit $$n=3$$ years

Step 1

Let us assume that the amount to be received by Kelly Cravens is A.

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

$$A=15,000\left(1+\frac{0.12}{3}\right)^{3 \times 3}$$

$$A=15,000(1+0.04)^{9}$$

$$A=15,000(1.04)^{9}$$

$$A=15,000(1.4230)$$

$$A=\ 21,345$$