Question

PLEASE help with question belowJaz needs to have $5500 in 7 years to purchase a new sound system for the theatre he is building in his new home. How much does he need to invest in a plan that pays 2.85%, compounded quarterly, to reach his goal?

Answer 1

Given:

a.) Jaz needs to have $5500 in 7 years.

b.) He will invest in a plan that pays 2.85%, compounded quarterly.

For us to be able to determine the principal amount needed to achieve $5500 in 7 years, we will be using the following formula:

`\text{ FV = P\lparen1 + }\frac{\text{ r }}{\text{ n }})^{\text{nt}}\text{ }`

Where,

FV = future value = $5500

P = principal amount = money invested

r = interest rate (in decimal) = 2.85 ÷ 100 = 0.0285

n = number of times interest applied per time period = quarterly = 4

t = time (in years) = 7

We get,

`\text{ 5500 = P\lparen1 + }(0.0285)/(4))^((4)(7))`
`\text{ P = }\frac{\text{ 5500 }}{(1\text{ + }(0.0285)/(4))^((4)(7))}`
`\text{ P = 4508.45919399624 }\approx\text{ \$4508.46}`

Therefore, Jaz will be needing to invest $4508.46 to achieve $5500 in 7 years.