Question

A friend wants to borrow money from you. He states that he will pay you $3,800 every 6 months for 13 years with the first payment exactly 6 years and six months from today. The interest rate is 6.1 percent compounded semiannually. What is the value of the payments today?

Answer #1

Sum of present value of N numbers of annuity A, at any time time t, when first annuity starts at t + 1 is given by:

V_{t} = A / R x [1 - (1 +
R)^{-N}] where R = interest rate per period

Here, payment frequency is semi annual. Hence, period is half year.

A = $ 3,800

R = semi annual interest rate = 6.1% / 2 = 3.05%

N = number of equally spaced annuities = 2 x 13 = 26

First annuity is paid out at the end of period t + 1 = 6.5 years away from now = 2 x 6.5 = 13 half years = 13 periods from now. Hence, t + 1 = 13, hence t = 12

Hence, V_{12} = A / R x [1 -
(1 + R)^{-N}] = $ 3,800 / 3.05% x [1 - (1 +
3.05%)^{-26}] = $ 67,543

Since we want the value today, we need to discount it further for 12 periods, hence

**Value today = V _{0}
= V_{t} / (1 + R)^{T} = $ 67,543 / (1 +
3.05%)^{12} = $ 47,098**

A friend wants to borrow money from you. He states that he will
pay you $3,400 every 6 months for 9 years with the first payment
exactly 7 years and six months from today. The interest rate is 5.7
percent compounded semiannually. What is the value of the payments
today?
$32,128.58
$33,021.49
$35,079.17
$31,070.77
$31,956.28

A friend wants to borrow money from you. He states that he will
pay you $3,600 every 6 months for 11 years with the first payment
exactly 4 years and six months from today. The interest rate is an
APR of 5.9 percent with semiannual compounding. What is the value
of the payments today?

Your friend wants to borrow money from you. He proposes to repay
his debt in 5 monthly installments of $200, starting from month 4
(i.e., the first payment will occur at the end of month 4). If the
monthly interest rate on your savings account is 1%, how much would
you lend your friend at most? Round your result to the nearest
cent, and do not use a $ sign (i.e., if the result is $1012.4671,
enter it as 1012.47).

Your friend wants to borrow money from you. He proposes to repay
his debt in 4 monthly installments of $100, starting this month
(i.e., the first payment will occur at the end of month 1). If the
monthly interest rate on your savings account is 1.5%, how much
would you lend your friend at most? Round your result to the
nearest cent, and do not use a $ sign (i.e., if the result is
$1012.4671, enter it as 1012.47)...

A friend asks to borrow $49 from you and in return will pay you
$52 in one year. If your bank is offering a. 6.1% interest rate on
deposits and loans: a. How much would you have in one year if you
deposited the $49 instead? b. How much money could you borrow
today if you pay the bank $52 in one year? c. Should you loan the
money to your friend or deposit it in the bank?
a. How...

You raise some money today from your friend. He agrees to loan
you the money you need, if you make payments of $40 a month for the
next one year. In keeping with his reputation, he requires that the
first payment be paid today. He also charges you 2 percent interest
per month. How much money are you borrowing?
ADue PV =

6. You loan some money to a friend and he agrees to pay
you $200 at the end of each month for the next 2.5 years. Using a
rate of 6.3%/year, calculate what this stream of anticipated
payments from your friend is worth in today’s dollar terms. In
other words, if your friend promises to make these payments, what
would be a fair amount to loan to him today?

A friend asks to borrow $46 from you, and in return will pay
you $49 in 1 year. If your bank is offering a 6.3% interest rate on
deposits and loans
How much money could you borrow today if you pay the bank $49
in one year?

a friend asks to borrow $51 from you and in return will pay you
$54
in one year. If your bank is offering a 6.4% interest rate on
deposits and loans:
a. How much would you have in one year if you deposited the $51
instead?
b. How much money could you borrow today if you pay the bank $54
in one year?
c. Should you loan the money to your friend or deposit it in
the bank?

A friend asks to borrow $49 from you and in return will pay you
$52 in one year. If your bank is offering a 6.5% interest rate on
deposits and loans:
A. How much would you have in one year if you deposited the $49
instead?
B. How much money could you borrow today if you pay the bank $52
in one year?
C. Should you loan the money to your friend or deposit it in the
bank?

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 46 minutes ago

asked 55 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago