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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 account that grows by $20 each year.

Which option will result in a better 18th birthday gift? Explain your reasoning.

Sagot :

Alyssah1025

Answer:

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

Step-by-step explanation:

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 = C.I=P(1+r) with an exponent of t

                                  C.I= 100(1 + 10.5 over 100)with an exponent of 18

                                  C.I= 100*6.0328

                                  C.I= $603.28

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 = 10+18*20

                                                                                         =460

Hope this helped <3

The child turns 18 years old, and the money in the account will be a birthday gift is a better 18th Birthday gift for a child by a Grandfather.

The amount deposited in the bank at the time of birth by Grandfather is $100.

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

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

What is the formula for compound interest?

Compound interest = C.I=P(1+r) with an exponent of t

C.I= 100(1 + 10.5 over 100)with an exponent of 18

C.I= 100*6.0328

C.I= $603.28

An account that grows by $20 each year

The amount credited in the account for 18 years = $20

The total amount after completion of 18 years = 10+18*20

 The total amount after completion of 18 years=460                                                                    

To learn more about the compound interest visit:

https://brainly.com/question/24924853

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