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 effective rate of interest corresponding to a nominal rate of $9 \% /$ year compounded annually, semiannually, quarterly, and monthly.

Five and a half years ago, Chris invested $$\$ 10,000$$ in a retirement fund that grew at the rate of \(10.82 \% /\) year compounded quarterly. What is his account worth today?

The proprietors of The Coachmen Inn secured two loans from Union Bank: one for $$\$ 8000$$ due in 3 yr and one for $$\$ 15,000$$ due in \(6 \mathrm{yr}\), both at an interest rate of \(10 \%\) /year compounded semiannually. The bank has agreed to allow the two loans to be consolidated into one loan payable in 5 yr at the same interest rate. What amount will the proprietors of the inn be required to pay the bank at the end of 5 yr? Hint: Find the present value of the first two loans.

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?

The Taylors have purchased a $$\$ 270,000$$ house. They made an initial down payment of $$\$ 30,000$$ and secured a mortgage with interest charged at the rate of \(8 \%\) /year on the unpaid balance. Interest computations are made at the end of each month. If the loan is to be amortized over \(30 \mathrm{yr}\), what monthly payment will the Taylors be required to make? What is their equity (disregarding appreciation) after 5 yr? After 10 yr? After 20 yr?