Question

Suppose you deposit $1,500 in a savings account that pays interest at an annual rate of 5%. If no money is added or withdrawn from the account, answer the following questions.

a. How much will be in the account after 4 years?
b. How much will be in the account after 16 years?
c. How many years will it take for the account to contain $2,000?
d. How many years will it take for the account to contain $2,500?

Answer 1

The solution is given below.

Explanation:

Given that

Deposited amount = $1,500

Rate of interest = 5%

We need to find out the following things

a. The account after 4 years i.e. future value

As we know that

Future value = Present value × (1 + rate)^time period

Future value = $1,500 × (1 + 0.05)^4

Future value = $1,500 × (1.05)^4

Future value = $1,823.26

b. The account after 16 years i.e. future value

As we know that

Future value = Present value × (1 + rate)^time period

Future value = $1,500 × (1 + 0.05)^16

Future value = $1,500 × (1.05)^16

Future value = $3,274.312

c. The number of years that contain the amount of $2,000

Here

PV = $1,500

FV = $2,000

PMT = $0

RATE = 5%

The following formula should be applied

= NPER(RATE;PMT;-PV;FV;TYPE)

After applying the above formula, the time period is 4.94 years

d. The number of years that contain the amount of $2,500

Here

PV = $1,500

FV = $2,000

PMT = $0

RATE = 5%

The following formula should be applied

= NPER(RATE;PMT;-PV;FV;TYPE)

After applying the above formula, the time period is 8.77 years