Question

You just received a bonus of ​$2,000.

a.Calculate the future value of ​$2,000​, given that it will be held in the bank for 6 years and earn an annual interest rate of 8 percent.

b. Recalculate part ​(a​) using a compounding period that is​ (1) semiannual and​ (2) bimonthly.

c. Recalculate parts ​(a​) and ​(b​) using an annual interest rate of 16 percent.

d. Recalculate part ​(a​) using a time horizon of 12 years at an annual interest rate of 8 percent.

e. What conclusions can you draw when you compare the answers in parts ​(c​) and ​(d​) with the answers in parts ​(a​) and ​(b​)?

Answer 1

a. Calculate the future value of ​$2,000​, given that it will be held in the bank for 6 years and earn an annual interest rate of 8 percent.

Solution:

Calculation of Future Value using Simple Interest Formula:

Given:

Present Value, PV= $ 2000

Number of Years, n = 6 Years

Annual rate of Interest, r = 8 % or 0.08

To Calculate:

Future Value of $ 2000 with 8% annual interest rate for 6 years:

Formula:

(Future Value using Simple Interest, as annual interest rate is mention in the question)

FV = PV × (1+ (r ×n))

Where:

FV = Future Value, PV = Present Value, r = Rate of Interest and n = Time period or Number of Years.

So, in this case Future Value will be calculated as follows:

FV = $ 2000 × (1 + (0.08×6))

= 2000 × (1 + 0.48)

= 2000 × 1.48

= $ 2960

Future Value = $ 2960

b. Recalculate part ​(a​) using a compounding period that is​ (1) semiannual and​ (2) bimonthly.

Solution:

1. Calculation of Future Value using Compound Interest Formula Compounded Semiannually:

Given:

Present Value, PV= $ 2000

Number of Years, n = 6 Years

Annual rate of Interest Compounded Semiannually, r = 8 % or 0.08

To Calculate:

Future Value of $ 2000 with 8% annual interest rate compounded semiannually for 6 years:

Formula:

(Future Value using Compound Interest Semiannually, as mention in the question)

FV = PV × 1 + r n

Where:

FV = Future Value, PV = Present Value, r = Rate of Interest and n = Time period or Number of Years.

Since the compound interest is compounded semiannually so we divide the interest rate by 2 and multiply n with 2 in order to calculate Future Value accurately:

Therefore,

r = 8 % / 2 = 4 % or 0.04

and n = 6 × 2 = 12 years

On putting the values in Formula, we get,

FV= 2000 × (1+ 0.04)12

= 2000 × 1.6010322186

Future Value = $ 3202.064

2) Calculation of Future Value using Compound Interest Formula Compounded Bimonthly:

Given:

Present Value, PV= $ 2000

Number of Years, n = 6 Years

Annual rate of Interest Compounded Bimonthly, r = 8 % or 0.08

To Calculate:

Future Value of $ 2000 with 8% annual interest rate compounded bimonthly for 6 years:

Formula:

(Future Value using Compound Interest Bimonthly, as mention in the question)

FV = PV × 1 + r n

Where:

FV = Future Value, PV = Present Value, r = Rate of Interest and n = Time period or Number of Years.

Since the compound interest is compounded bimonthly so total number of compounding in a year is 24 i.e. 2 × 12, hence we divide the interest rate by 24 and multiply n with 24 in order to calculate Future Value accurately:

Therefore,

r = 8 % / 24 = 0.0033

and n = 6 × 24 = 144

On putting the values in Formula, we get,

FV= 2000 × (1+ 0.0033)144

= 2006

Future Value = $ 2006

c) Recalculate parts ​(a​) and ​(b​) using an annual interest rate of 16 percent.

Solution:

1. Calculation of Future Value using Simple Interest Formula with time of 6 years and interest rate of 16 percent:

Given:

Present Value, PV= $ 2000

Number of Years, n = 6 Years

Annual rate of Interest, r = 16 % or 0.16

To Calculate:

Future Value of $ 2000 with 16% annual interest rate for 6 years:

Formula:

(Future Value using Simple Interest, as annual interest rate is mention in the question)

FV = PV × (1+ (r ×n))

Where:

FV = Future Value, PV = Present Value, r = Rate of Interest and n = Time period or Number of Years.

So, in this case Future Value will be calculated as follows:

FV = $ 2000 × (1 + (0.16×6))

= 2000 × (1 + 0.96)

= 2000 × 1.96

= $ 3920

Future Value = $ 3920

d. Recalculate part ​(a​) using a time horizon of 12 years at an annual interest rate of 8 percent.

Solution:

Calculation of Future Value using Simple Interest Formula with time of 12 years and interest rate of 8 percent:

Given:

Present Value, PV= $ 2000

Number of Years, n = 12 Years

Annual rate of Interest, r = 8 % or 0.08

To Calculate:

Future Value of $ 2000 with 8 % annual interest rate for 12 years:

Formula:

(Future Value using Simple Interest, as annual interest rate is mention in the question)

FV = PV × (1+ (r ×n))

Where:

FV = Future Value, PV = Present Value, r = Rate of Interest and n = Time period or Number of Years.

So, in this case Future Value will be calculated as follows:

FV = $ 2000 × (1 + (0.08×12))

= 2000 × (1 + 0.96)

= 2000 × 1.96

= $ 3920

Future Value = $ 3920