MATH SOLVE

4 months ago

Q:
# How do I solve this?Jacob is saving up for a down payment on a car. He plans to invest $2,000 at the end of every year for 5 years. If the interest rate on the account is 2.25% compounding annually, what is the present value of the investment?a. $5,666.58b. $10,461.24c. $9,358.91d. $37,731.88

Accepted Solution

A:

To compute the value of investment in 5 years. We use compounded annually equation. And add 2000 Yearly to the compounded value

A = P * (1 + (r/n))^(n*t)

A = total amount = Unknown

P = principal or amount of money deposited, = 2000 usd

r = annual interest rate = 2.25%

n = number of times compounded per year = 1

t = time in years = 5

Solution

Year1 : A1 = 2000 * (1 +(0.025/1))^(1*1) = 2045

Year2 : A2 = (2000+2045)*(1 +(0.025/1))^(1*1) = 4136.01

Year3 : A3 = (2000+4136.01))*(1 +(0.025/1))^(1*1) = 6274.07

Year4 : A4 = (2000+6274.07 ))*(1 +(0.025/1))^(1*1) = 8460.24

Year5 : A5 = (2000+8460.24 ))*(1 +(0.025/1))^(1*1) = 10695.6

A = P * (1 + (r/n))^(n*t)

A = total amount = Unknown

P = principal or amount of money deposited, = 2000 usd

r = annual interest rate = 2.25%

n = number of times compounded per year = 1

t = time in years = 5

Solution

Year1 : A1 = 2000 * (1 +(0.025/1))^(1*1) = 2045

Year2 : A2 = (2000+2045)*(1 +(0.025/1))^(1*1) = 4136.01

Year3 : A3 = (2000+4136.01))*(1 +(0.025/1))^(1*1) = 6274.07

Year4 : A4 = (2000+6274.07 ))*(1 +(0.025/1))^(1*1) = 8460.24

Year5 : A5 = (2000+8460.24 ))*(1 +(0.025/1))^(1*1) = 10695.6