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when a child is born, her grandfather decides to put $100 in an account that earns interest. he plans to make no other deposits or withdrawals for 18 years. when the child turns 18 years old, the money in the account will be a birthday gift. the grandfather is choosing between two options:

Option 1: An account that grows by 10.5% each year

Option 2: An acount that grows by $20 each year.

which option will result in a better 18th birthday gift? explain your reasoning.

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Respuesta :

Answer:

We get that option (1) is a better 18th Birthday gift of child by Grandfather.

Step-by-step explanation:

Given that,

Amount deposited in bank at time of birth by Grandfather is $100.

And there is no other deposits and withdrawals for 18 years.

So,

                           Principal amount =$100

                                              Time = 18 years

               Rate of interest of bank = 10.5%

Option 1:- An account That grows by 10.5% each year

we know that Bank give compound interest on the deposit amount

then                   Compound interest = [tex]C.I = P(1+r)^{t}[/tex]

∴                                                [tex]C.I = 100(1+\frac{10.5}{100} )^{18}[/tex]

                                                  [tex]C.I = 100 \times6.0328[/tex]

                                                   [tex]C.I=\$603.28[/tex]

Option 2:- An account that grows by $20 each year

Here,

                    Amount credited in account for 18 years = $20

So,                Total amount after completion of 18 years = [tex]100+18\times20[/tex]

                                                                                           =[tex]\$460[/tex]

Hence,

We get that option (1) is a better 18th Birthday gift of child by Grandfather.