Question

Jenny and Dan want to save for an RV. They estimate that they will need $15,000 in 8 years. They can get 3% interest compounded semiannually. How much would they need to deposit now in order to have $15,000 in 8 years?

Answer 1

Answer: P = 11820.47

Explanation:

Formula for compound interest:

`A = P(1+(r)/(n) )^(nt)`

A = after amount =15000

P = Principal, initial/deposit amount = find this

r = rate in decimal form = .03

n = number of times it compounds in 1 year = 2 >semiannually

t = time in years > 8

`15000 = P(1+(.03)/(2) )^((2)(8))`

`15000 = P(1.015 )^(16)`

15000 = P(1.015 )^{16}

15000 = P(1.26899)

P = 11820.47

Answer 2

$11820.466 ROUNDS TO $11820.47

Explanation:

Using the compound interest formula:

X = P(1+r/n)^(nt)

where X = desired amount (15,000 in this case)

P = principle or initial amount

r = interest rate (0.03 or 3% in this case)

n = number of times the interest is compounded each year (2 in this case because interest is compounded semiannually)

t = time in years

you can begin to plug in your numbers

15,000 = P(1+0.03/2)^(2*8) --> this will show you that they are looking to have 15,000 by the end of the 8 years, at a rate of 3% (0.03) with interest compounded semiannually

from here you can simplify (1+0.03/2)^(2*8) to 1.27 (full decimal = 1.26898554765)

and then you have

15,000 = P * 1.26898554765

then divide 15,000 by 1.26898554765

and get P = 11820.466, which rounds to $11820.47

hope this helps!