Question

1. What is the balance in a bank account at the end of 10 years if $2,500 is deposited today and the account earnd 4% interest compounded annually? Quarterly?

2. If you deposit $10 in an account that pays 5% inteterst, compounded annually, how much will you have at the end of 10 years? 20 years? 50 years?

3. Suppose you deposit $100,000 in an account today that pays 6% interest, compounded annually. How long does it take before the balance in your account is $500,000?

Answer 1

Solution:

1) We use the formula:

A=P(1+r/100)ⁿ

Where A = future value

p = present value

r = rate of interest

n = time of period

A = $2500 * (1.04)¹⁰

    = $2500 * 1.480244285

    =$3700.61(approx)

2) Calculation of future worth

Amount deposited = $10

Interest rate = 5%

Future worth is calculated by the following

Fw =Principal *(1 + interest rate)ⁿ

where n = no of years compounded

a) N = 10 years            b) N = 20 years                            c) N = 50 years

    =10*(1.05)¹⁰                          =10*(1.05)²⁰                                    =10*(1.05)⁵⁰

    = 10*1.628895                      =10*2.65329                                    =10*11.46739

   =13.28895                             =26.5329 =114.6739

3) We can use future value of a sum formula no of years required to turn 100,000 into 500,000

Fv = p *(1+r)ⁿ

Note:

Fv = 500,000

r = 0.06

p = 100,000

500,000 = 100,000 *(1+0.06)ⁿ                               

500,000 = 100,000*(1.06)ⁿ

n = 27.62

Total years required = 27.62 years