Question

14. Your grandfather put some money into an account for you on the day you were born. You are now 18 years old and are allowed to withdraw the money. The account currently has $7,527 in it and pays an interest rate of 9%.

a. How much money would be in the account if you left the money there until your 25th​ birthday?

b. What if you left the money until your 65th​ birthday?

c. How much money did your grandfather originally put into the​ account?

Answer 1

a) The till 24th birthday there is a period of 7 years so we need to find the FV after 7 years we need to solve the below equation:

We are given the following information

PV	7527
r	9.00%
n	7
frequency	1

We need to solve the following equation to arrive at the required FV

FV = PV X (1+r)"

FV = 7527 x (1 + 0.09)

FV = 13759.65

So the FV is $13759.65

b) Till 65th birthday 47 years are there

We are given the following information:

PV	7527
r	9.00%
n	47
frequency	1

We need to solve the following equation to arrive at the required FV

FV = PV X (1+r)"

FV = 7527 x (1 + 0.09)47

F = 432182.64

So the FV is $432182.64

c) In 18 years the account amounted to 7527 at 9% interest rate

We are given the following information:

FV	7527
r	9.00%
n	18
frequency	1

We need to solve the following equation to arrive at the required PV

FV = PV X (1+r)"

7527 = PV X (1+0.09)18

PV = 1,595.68

So the amount put in by the grandfather is 1595.65