Bennington Company has borrowed a certain amount from the bank that it will repay in 24 monthly installments. The bank charges 6% interest annually on this loan and the monthly payment is $6000. Find the amount of loan.
Answer
Monthly
interest = 6%/12 = 0.005
Number of
months = 24
monthly payment = 6000
PV = 6000 x
[1-1.005^-24]/0.005
PV =
135377.2
Suppose you are a property owner and you are collecting rent for an apartment. The tenant has signed a one-year lease with $600 a month rent, payable in advance. Find the present value of the lease contract if the discount rate is 12% per year.
Answer
Here monthly rent =$600, Number of months = 12 ,
We use this formula here
Present value of the lease contract = 600 + 600 x
[1-(1.01)^-11]/0.01
Present value of the lease contract = 6820.58
Here another way to do it this one:
Suppose you want to accumulate $25,000 as down payment on a house and the best you can do is to put aside $200 a month. If you deposit this amount at the beginning of each month in an account that credits 0.75% interest monthly, how long will it take you to attain your goal?
Solution
Sn= down
payment =25,000 , interest monthly = 0.75% = 0.0075
25,000 = 200(1.0075)^n+
200(1.0075)^n−1 + ... + 100(1.0075)
25,000 = 200(1.0075)^n+
200(1.0075)^n−1 + ... +200(1.0075)
Here a = 200(1.0075)^n,
x =1/1.0075, Sn= 25,000
25,000 = 200(1.0075)^n
[1-(1/1.0075^n)]/1-1/1.0075
25,000 = 200(1.0075)^n
-200/0.007444169
25,000 x 0.007444169
= 200(1.0075)^n -200
186.10 = 200(1.0075)^n
-200
186.10 +200 = 200(1.0075)^n
386.10 =200(1.0075)^n
386.10 /200 =
(1.0075)^n
1.930521 = (1.0075)^n
Taking ln
both sides, we get
Ln(1.930521)
= n ln(1.0075)
N = Ln(1.930521)/
ln(1.0075)
N = 88
months
Suppose you want to accumulate $10,000 for a down payment for a house. You will deposit $400 at the beginning of every month in an account that credits interest monthly at the rate of 0.6% per month. How long will it take you to achieve your goal?
Answer
Here
FV = 10000 ,
Per moth payments = 400, interest monthly = 0.6% =0.006
Number of
years =?
10,000 = 400(1.006)+
100(1.0075)n−1 + ... + 100(1.0075)
10,000 =
400(1.006)^n + 400(1.006)^n-1+…..+400(1.006)
Here a = 400(1.006)^n
, x =1/1.006, Sn= 10,000
10,000 =
400(1.006)^n [1-1/1.006^n]/1-1/1.006
Now
1/1.006^n =
1.006^-n & 1/1.006 = 1.006^-1
10,000 = 400
(1.006)^n [1-1.006^-n]/1-1.006^-1
10,000 = 400(1.006)^n
-400]/1-1.006^-1
Here
1-1.006^-1 =
0.005964
10,000 =400(1.006)^n
-400]/ 0.005964
10,000 x 0.005964
= 400(1.006)^n -400
59.64 +400 = 400(1.006)^n
Divided by
400 both sides
459.64/400 = 400(1.006)^n/400
1.149105 =
1.006^n
Take ln both
side
Ln(1.149105)
= n ln(1.006)
Ln(1.149105)/
ln(1.006) =n
n = 23.23 is
almost equal to 24 months
You have started a job with an annual salary of $48,000. You will get the paycheck at the end of each month, and your deductions for taxes will be 34%. Using a discount rate of 0.8% per month, find the present value of the take home pay for the whole year.
Answer
Monthly interest rate = 0.8% = 0.008
Monthly salary = 48000/12 = 4000
Monthly salary after tax = 4000 x (1-0.34) = 2640
So Answer is 30,092.34
You have decided to put $130 in a savings account at the end of each month. The savings account credits interest monthly, at the annual rate of 6%. How much money is in your account after 6 years?
Solution
monthly rate
of interest = 6%/12 = 0.005
Number of
months = 6 x 12 = 72
Deposit made
at the end of each month so, Number of years = 72-1 = 71
S = 130 (1.005)^71
+ 130 (1.005)^70+ …….+130 (1.005)
Here , a=130
(1.005)^71 and x = 1/1.005
FV = 130+[130
(1.005)^71 [1-(1/1/1.005^71)] / 1-1/1.005 ]
Now,
1/1.005^71 = 1.005^-71 (Simple math)
FV = 130+130
(1.005)^71 [1-1.005^-71]/1-1.005^-1
FV = 11,233.15
