Question

karl opens a savings account with 2500.Hedeposits1500 every year into the account that has a 0.75% interest rate, compounded monthly. If he doesn't withdraw any money, what will the account balance be in 10 years

Answer 1

Answer:

28707.80 is the account balance after 10 years.

Explanation:

In his question we have two parts of the problem  the first one is a single deposit of 2500 in which we will find its future value after 10 years by using the future value formula which is Fv = Pv(1+i)^n , where

Fv is the future value after 10 years of saving the amount which we are calculating.

Pv is the present value initial investment of 2500

i is the annual interest rate which will be 0.75% x 12 = 9% as we are given a rate which is for monthly compounding.

n is the number of years the 2500 is saved up for.

Then we substitute these values to the above mentioned formula:

Fv = 2500(1 +9%)^10

Fv = 5918.41

now we will solve the second part of the question which involves 1500 deposited every year which this is an annuity part of the question where periodic payments are made constantly over 10 years for a certain future amount. which the formula is Fv = C[((1+i)^n -1)/i] , where

Fv is the future value of saving 1500 per year for 10 years

C is the periodic saving which is 1500

i is the annual interest rate of 9% as the 1500 is saved per year

n is the number of periods the 1500 is deposited for which is 10 years'

now we substitute to the above mentioned formula to find the future value:

Fv =  1500[((1 + 9%)^10 -1)/9%]

Fv =22789.39 .

now we will combine both future values to find the account balance after 10 years which will be 22789.39+ 5918.41 = 28707.80 rounded off to two decimal places.