Question

Account A pays 13.8% interest per year. Account B pays 13.5% interest per year, compounded monthly. Account C pays 13% interest per year, compounded daily. For each account, determine the value of your investment after 12 years.

Answer 1

Answer:

1. Future value (FV) = $4,717

2. Future value (FV) = $5,189

3. Future value (FV) = $5,237

Explanation:

Requirement 1

Assume that the present value of the investment is $1,000.

We know, Compounding yearly,

FV = PV*(1 + i)^n

Given,

Present value (PV) = $1,000

Interest rate, i = 13.8% = 0.138

number of periods, n = 12 years

We have to calculate the future value of the investment.

Therefore,

FV = $1,000 × $(1 + 0.138)^{12}$

or, FV = $1,000 × $1.138^{12}$

or, FV = $1,000 × 4.7174

Therefore, Future value (FV) = $4,717

Requirement 2

Again, Assume that the present value of the investment is $1,000.

We know, Compounding monthly,

FV = PV × $(1 + \frac{i}{m})^{m*n}$

Given,

Present value (PV) = $1,000

Interest rate, i = 13.8% = 0.138

number of periods, n = 12 years

compounding period (monthly), m = 12

We have to calculate the future value of the investment.

Therefore,

FV = $1,000 × $(1 + \frac{0.138}{12})^{12*12}$

or, FV = $1,000 × $(1 + 0.0115)^{144}$

or, FV = $1,000 × $1.0115^{144}$

or, FV = $1,000 × 5.1890

Therefore, Future value (FV) = $5,189

Requirement 3

Again, Assume that the present value of the investment is $1,000.

We know, Compounding daily,

FV = PV × $(1 + \frac{i}{m})^{m*n}$

Given,

Present value (PV) = $1,000

Interest rate, i = 13.8% = 0.138

number of periods, n = 12 years

compounding period (daily), m = 365

We have to calculate the future value of the investment.

Therefore,

FV = $1,000 × $(1 + \frac{0.138}{365})^{365*12}$

or, FV = $1,000 × $(1 + 0.000378)^{4,380}$

or, FV = $1,000 × $1.000378^{4380}$

or, FV = $1,000 × 5.2367

Therefore, Future value (FV) = $5,237