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

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

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

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

Step-by-step 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 + (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 + (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 + (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 + (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