Question

Mike needs $41,300 to purchase a boat. How much money will he need to invest today in a savings account earning 3.7% interest, compounding quarterly, to have enough money to purchase the boat in 15 years?

Answer 1

$4,669.01

$39,071.30

$35,624.90

$23,769.75

Answer 2

the formula for compound interest is :
\(I = P (1+r/4)^{4n} -P\)
where P is the principal amount,
n= time period in years and r= rate of interest.

Answer 3

p= 41,300 r= 0.00925 right?

Answer 4

and the final amount is say, A = I+P = \((1+r/4)^{4n} \)
not really,
he needs final amount as 41300 , so A = 41,300

Answer 5

r= 3.7% = 0.037

Answer 6

but you divide r/4 right?

Answer 7

so whats P?

Answer 8

so, r/4 = 0.037/4=0.00925

Answer 9

P is money invested today which you need to find out

Answer 10

oh ok. so how do i make that a formula?

Answer 11

you plug in all the values first,
n= 15

Answer 12

its nt right? so 15x4=60

Answer 13

the ecponent = 4n = 60 yes

Answer 14

ok so whats next?

Answer 15

what u got after plugging in ?

Answer 16

41300(1+0.00925)^60?

Answer 17

41300 = P (1+0.00925)^60

Answer 18

use calculator for this
(1+0.00925)^60

Answer 19

1.7375

Answer 20

yes,
41300 = P *1.7375
now can you find P ?

Answer 21

do i divide 41300/1.7375

Answer 22

yes

Answer 23

awesome so i got 23,769.78

Answer 24

the answer is off by a few cents but that doesnt really matter, right?

Answer 25

i too get the same :)

Answer 26

yes, it doesn't. i clculated it and got 23769.747

Answer 27

ok cool. can you help me with something else please?

Answer 28

sure, :)

Answer 29

thanks :) ok so
Julianne wants to take a trip around the world. She plans to deposit $175 at the beginning of each month into an investment with a 3.25% interest rate, compounded monthly. How much will she have in the account after 12 years?
30,770.00

$30,853.33

$533,286.11

$550,617.91

Answer 30

\(A= P (1+r/2)^{2n} \)

Answer 31

same as before?

Answer 32

the formula changed for monthly...

Answer 33

now you have to find A

Answer 34

P=175?

Answer 35

yes, r = 3.25 % = 0.0325

Answer 36

n=12

Answer 37

r=0.002708

Answer 38

why ?

Answer 39

because its divided by 12

Answer 40

its r/2 , not r/12

Answer 41

If you are making monthly deposits you use a more complicated formula
FV = PMT * ( ( (1 + i)^n - 1) / i )

Answer 42

oh, wait i am sorry, its r/12 only

Answer 43

\(A= P (1+r/12)^{12n}\)

Answer 44

oh ok. @phi what are the values of PMT?

Answer 45

PMT is the payment $175

Answer 46

@hartnn its 12x12=144 for nt, right?

Answer 47

yes.

Answer 48

ok so 175(1+0.002708)^144?

Answer 49

i believe that would give you the answer...

Answer 50

im getting 258.34

Answer 51

me too

Answer 52

this problem is different from the 1st one. You are making regular deposits every month of 175
even with no interest you would expect 175*144
with compounded monthly interest, you have to use the formula I posted up above

Answer 53

so i multiply 175*144 and i get 25200.

Answer 54

would that be the PMT?

Answer 55

\[ FV = pymt\cdot \frac{ (1+i)^n -1}{i} \]

Answer 56

where i is the monthly interest 0.0325/12
and n is in months 12years * 12 months/year = 144

Answer 57

whats the payment?

Answer 58

She plans to deposit $175 at the beginning of each month

Answer 59

so i multiply 175 by 144?

Answer 60

no, you have to use the formula. Do it step by step.
\[FV = pymt\cdot \frac{ (1+i)^n -1}{i} \]

replace all the letters with numbers: you know pymt is 175
you know i and you you know n

Answer 61

im not getting it

Answer 62

First step, what is i for this problem ?

Answer 63

0.0325/12= 0.002708333

Answer 64

so we put that into the formula to get
\[ FV = pymt\cdot \frac{ (1+i)^n -1}{i} \]
\[ FV = pymt\cdot \frac{ (1+0.002708333)^n -1}{0.002708333} \]

Answer 65

what is n? (in months)
what is pymt ?

Answer 66

n=12 pymt= 175

Answer 67

remember, the term is 12 years, monthly
it is 144 months
n is 144

so now we have
\[ FV =175\cdot \frac{ (1.002708333)^{144} -1}{0.002708333} \]

notice I simplified 1+0.002708333 to 1.002708333

Answer 68

now time to get out the calculator

Answer 69

30,769.99 rounded up is 30,770 :)

Answer 70

yes, success!

Answer 71

lol thanks. do you mind helping some more?

Answer 72

aww ok. well thanks so much.