Chapter 4

Find the periodic payment \(R\) required to amortize a loan of \(P\) dollars over \(t\) yr with interest charged at the rate of \(r \% /\) year compounded \(m\) times a year. $$ P=100,000, r=8, t=10, m=1 $$

Find the amount (future value) of each ordinary annuity. $$\$ 1000$$ /year for 10 yr at \(10 \% /\) year compounded annually

Find the accumulated amount \(A\) if the principal \(P\) is invested at the interest rate of \(r /\) year for \(t\) yr. $$ P=\$ 1000, r=7 \%, t=8, \text { compounded annually } $$

Find the simple interest on a $$\$ 500$$ investment made for 2 yr at an interest rate of \(8 \% /\) year. What is the accumulated amount?

Find the periodic payment \(R\) required to amortize a loan of \(P\) dollars over \(t\) yr with interest charged at the rate of \(r \% /\) year compounded \(m\) times a year. $$ P=40,000, r=3, t=15, m=2 $$

Find the amount (future value) of each ordinary annuity. $$\$ 1500 /$$ semiannual period for 8 yr at \(9 \%\) /year compounded semiannually

Find the simple interest on a $$\$ 1000$$ investment made for 3 yr at an interest rate of \(5 \% /\) year. What is the accumulated amount?

Find the periodic payment \(R\) required to amortize a loan of \(P\) dollars over \(t\) yr with interest charged at the rate of \(r \% /\) year compounded \(m\) times a year. $$ P=5000, r=4, t=3, m=4 $$

Find the amount (future value) of each ordinary annuity. $$ \text { \$1800/quarter for } 6 \text { yr at } 8 \% \text { year compounded quarterly } $$

Find the accumulated amount at the end of \(9 \mathrm{mo}\) on an $$\$ 800\( \)deposit in a bank paying simple interest at a rate of \(6 \% /\) year.

Find the periodic payment \(R\) required to amortize a loan of \(P\) dollars over \(t\) yr with interest charged at the rate of \(r \% /\) year compounded \(m\) times a year. $$ P=16,000, r=9, t=4, m=12 $$

Find the amount (future value) of each ordinary annuity. $$\$ 500 /$$ semiannual period for \(12 \mathrm{yr}\) at \(11 \% / \mathrm{year}\) compounded semiannually

Find the accumulated amount at the end of \(8 \mathrm{mo}\) on a $$\$ 1200$$ bank deposit paying simple interest at a rate of \(7 \% /\) year.

Find the periodic payment \(R\) required to amortize a loan of \(P\) dollars over \(t\) yr with interest charged at the rate of \(r \% /\) year compounded \(m\) times a year. $$ P=25,000, r=3, t=12, m=4 $$

Find the amount (future value) of each ordinary annuity. $$ \text { \$600/quarter for } 9 \text { yr at } 12 \% / \text { year compounded quarterly } $$

If the accumulated amount is $$\$ 1160$$ at the end of \(2 \mathrm{yr}\) and the simple rate of interest is \(8 \% /\) year, then what is the principal?

Find the periodic payment \(R\) required to amortize a loan of \(P\) dollars over \(t\) yr with interest charged at the rate of \(r \% /\) year compounded \(m\) times a year. $$ P=80,000, r=10.5, t=15, m=12 $$

Find the amount (future value) of each ordinary annuity. $$ \$ 150 / \text { month for } 15 \text { yr at } 10 \% / \text { year compounded monthly } $$

A bank deposit paying simple interest at the rate of \(5 \% /\) year grew to a sum of $$\$ 3100$$ in 10 mo. Find the principal.

Find the periodic payment \(R\) required to amortize a loan of \(P\) dollars over \(t\) yr with interest charged at the rate of \(r \% /\) year compounded \(m\) times a year. $$ P=80,000, r=10.5, t=30, m=12 $$

How many days will it take for a sum of $$\$ 1000$$ to earn $$\$ 20$$ interest if it is deposited in a bank paying ordinary simple interest at the rate of \(5 \% /\) year? (Use a 365 -day year.)

How many days will it take for a sum of $$\$ 1500$$ to earn $$\$ 25$$ interest if it is deposited in a bank paying \(5 \% /\) year? (Use a 365-day year.)

Find the periodic payment \(R\) required to accumulate a sum of \(S\) dollars over \(t\) yr with interest earned at the rate of \(r \% /\) year compounded \(m\) times a year. $$ S=20,000, r=4, t=6, m=2 $$

A bank deposit paying simple interest grew from an initial sum of $$\$ 1000$$ to a sum of $$\$ 1075$$ in 9 mo. Find the interest rate.

Find the periodic payment \(R\) required to accumulate a sum of \(S\) dollars over \(t\) yr with interest earned at the rate of \(r \% /\) year compounded \(m\) times a year. $$ S=40,000, r=4, t=9, m=4 $$

Find the present value of each ordinary annuity. $$\$ 1200 /$$ semiannual period for 6 yr at \(10 \%\) lyear compounded semiannually

Determine the simple interest rate at which $$\$ 1200$$ will grow to $$\$ 1250$$ in 8 mo.

Find the periodic payment \(R\) required to accumulate a sum of \(S\) dollars over \(t\) yr with interest earned at the rate of \(r \% /\) year compounded \(m\) times a year. $$ S=100,000, r=4.5, t=20, m=6 $$

Find the periodic payment \(R\) required to accumulate a sum of \(S\) dollars over \(t\) yr with interest earned at the rate of \(r \% /\) year compounded \(m\) times a year. $$ S=120,000, r=4.5, t=30, m=6 $$

Find the present value of each ordinary annuity. $$\$ 3000 /$$ semiannual period for 6 yr at \(11 \%\) year compounded semiannually

Find the accumulated amount \(A\) if the principal \(P\) is invested at the interest rate of \(r /\) year for \(t\) yr. $$ P=\$ 1000, r=8 \frac{1}{2} \%, t=6, \text { compounded annually } $$

Find the periodic payment \(R\) required to accumulate a sum of \(S\) dollars over \(t\) yr with interest earned at the rate of \(r \% /\) year compounded \(m\) times a year. $$ S=250,000, r=10.5, t=25, m=12 $$

Find the accumulated amount \(A\) if the principal \(P\) is invested at the interest rate of \(r /\) year for \(t\) yr. $$ P=\$ 2500, r=7 \%, t=10, \text { compounded semiannually } $$

Find the periodic payment \(R\) required to accumulate a sum of \(S\) dollars over \(t\) yr with interest earned at the rate of \(r \% /\) year compounded \(m\) times a year. $$ S=350,000, r=7.5, t=10, m=12 $$

Find the accumulated amount \(A\) if the principal \(P\) is invested at the interest rate of \(r /\) year for \(t\) yr. $$ P=\$ 2500, r=9 \%, t=10 \frac{1}{2}, \text { compounded semiannually } $$

Suppose payments were made at the end of each quarter into an ordinary annuity earning interest at the rate of \(10 \% /\) year compounded quarterly. If the future value of the annuity after \(5 \mathrm{yr}\) is \(\$ 50,000\), what was the size of each payment?

If a merchant deposits $$\$ 1500$$ at the end of each tax year in an IRA paying interest at the rate of \(8 \% /\) year compounded annually, how much will she have in her account at the end of 25 yr?

Find the accumulated amount \(A\) if the principal \(P\) is invested at the interest rate of \(r /\) year for \(t\) yr. $$ P=\$ 12,000, r=8 \%, t=10 \frac{1}{2}, \text { compounded quarterly } $$

If Jackson deposits $$\$ 100$$ at the end of each month in a savings account earning interest at the rate of \(8 \%\) /year compounded monthly, how much will he have on deposit in his savings account at the end of \(6 \mathrm{yr}\), assuming that he makes no withdrawals during that period?

Find the accumulated amount \(A\) if the principal \(P\) is invested at the interest rate of \(r /\) year for \(t\) yr. $$ P=\$ 42,000, r=7 \frac{3}{4} \%, t=8, \text { compounded quarterly } $$

Suppose payments will be made for \(6 \frac{1}{2}\) yr at the end of each semiannual period into an ordinary annuity earning interest at the rate of \(7.5 \% /\) year compounded semiannually. If the present value of the annuity is $$\$ 35,000$$, what should be the size of each payment?

Linda has joined a "Christmas Fund Club" at her bank. At the end of every month, December through October inclusive, she will make a deposit of $$\$ 40$$ in her fund. If the money earns interest at the rate of \(7 \% /\) year compounded monthly, how much will she have in her account on December 1 of the following year?

Find the accumulated amount \(A\) if the principal \(P\) is invested at the interest rate of \(r /\) year for \(t\) yr. $$ P=\$ 150,000, r=14 \%, t=4, \text { compounded monthly } $$

Suppose payments will be made for \(9 \frac{1}{4}\) yr at the end of each month into an ordinary annuity earning interest at the rate of \(6.25 \% /\) year compounded monthly. If the present value of the annuity is $$\$ 42,000$$, what should be the size of each payment?

Robin, who is self-employed, contributes $$\$5000$$/year into a Keogh account. How much will he have in the account after \(25 \mathrm{yr}\) if the account earns interest at the rate of \(8.5 \% /\) year compounded yearly?

A sum of $$\$ 100,000$$ is to be repaid over a 10 -yr period through equal installments made at the end of each year. If an interest rate of \(10 \% /\) year is charged on the unpaid balance and interest calculations are made at the end of each year, determine the size of each installment so that the loan (principal plus interest charges) is amortized at the end of \(10 \mathrm{yr}\).

As a fringe benefit for the past 12 yr, Colin's employer has contributed $$\$ 100$$ at the end of each month into an employee retirement account for Colin that pays interest at the rate of \(7 \% /\) year compounded monthly. Colin has also contributed $$\$ 2000$$ at the end of each of the last 8 yr into an IRA that pays interest at the rate of \(9 \% /\) year compounded yearly. How much does Colin have in his retirement fund at this time?

Find the accumulated amount \(A\) if the principal \(P\) is invested at the interest rate of \(r /\) year for \(t\) yr. $$ P=\$ 150,000, r=12 \%, t=3, \text { compounded daily } $$

What monthly payment is required to amortize a loan of $$\$ 30,000$$ over \(10 \mathrm{yr}\) if interest at the rate of \(12 \% /\) year is charged on the unpaid balance and interest calculations are made at the end of each month?

The Pirerras are planning to go to Europe 3 yr from now and have agreed to set aside $$\$ 150 /$$ month for their trip. If they deposit this money at the end of each month into a savings account paying interest at the rate of \(8 \% /\) year compounded monthly, how much money will be in their travel fund at the end of the third year?