BA II Plus calculator for SOA Exam FM

1. Clear the TVM worksheet first

Before every interest-theory problem, clear the five TVM registers so a stale FV from your last annuity does not leak into the next one. On a physical BA II Plus that is 2ND then FV (CLR TVM).

2. Keep one payment per period

Exam FM problems are stated per period at an effective rate, so set P/Y and C/Y to 1. Then I/Y is the effective rate per period and N is the number of periods — the annuity-immediate and annuity-due formulas map straight onto the keys.

3. Enter the effective rate and term

For a 10-period annuity valued at an effective 6% per period, store 10 in N and 6 in I/Y. The BA II Plus treats I/Y as an effective rate once P/Y and C/Y are both 1.

4. Mind the cash-flow signs

Payments received and payments made take opposite signs. Enter a level annuity payment of 1000 as PMT, leave FV at 0, and CPT PV returns a negative present value — the price you would pay to receive that annuity-immediate.

5. Switch to BGN for an annuity-due

Interest theory calls a payment at the start of each period an annuity-due. Toggle the calculator to BGN mode (2ND PMT) and the same keystrokes value the due form, one period earlier than the immediate form.

6. Read the outstanding balance

After solving a loan payment, the amortization worksheet gives the outstanding balance after any period. That balance equals the prospective present value of the remaining payments — the same number you would get from the retrospective method.

An annuity-immediate pays 1,000 at the end of each year for 10 years. At an annual effective rate of 6%, what is its present value?

Set P/Y = C/Y = 1 so I/Y is the effective per-period rate. Store N = 10, I/Y = 6, PMT = 1000, FV = 0 in END mode, then CPT PV.

This is 1,000 times a-angle-10 at 6%. The value is negative because it is the price paid to acquire the annuity.

A saver deposits 500 at the beginning of each year for 15 years earning 5% annual effective. What is the accumulated value at the end of year 15?

Switch to BGN for the annuity-due. Set P/Y = C/Y = 1, store N = 15, I/Y = 5, PMT = 500, PV = 0, then CPT FV.

This is 500 times s-double-dot-angle-15 at 5%. With positive deposits the calculator returns the accumulated value with the opposite sign.

You must accumulate 100,000 in a sinking fund over 8 years. The fund earns 7% annual effective and deposits are made at the end of each year. What level deposit is required?

Set the target as the future value. Store N = 8, I/Y = 7, PV = 0, FV = 100000 in END mode, then CPT PMT.

The deposit equals 100,000 divided by s-angle-8 at 7%. It is negative because each deposit is an outflow into the fund.

A 20,000 loan at 8% annual effective is repaid with 10 equal year-end payments. What is the outstanding balance immediately after the 4th payment?

Store N = 10, I/Y = 8, PV = 20000, FV = 0 and CPT PMT to get the level payment (-2,980.59). Then open 2ND AMORT and read the balance at period 4.

The prospective outstanding balance is the payment times a-angle-6 at 8%, and it matches the retrospective calculation to the cent.

A 10-year, 1,000 par bond pays an 8% annual coupon in semiannual installments and is priced to yield 6% convertible semiannually. What is its price?

Work in semiannual periods: N = 20, I/Y = 3 per period, coupon PMT = 40, redemption FV = 1000, then CPT PV.

The 4% per-period coupon exceeds the 3% per-period yield, so the bond sells above par at a premium.

A rate is quoted as a nominal 8% convertible quarterly. What is the equivalent annual effective rate?

Use the interest-conversion worksheet (2ND ICONV): enter the nominal rate 8 with 4 compounding periods per year and read the effective rate.

Equivalently (1 + 0.08/4)^4 - 1 = 8.2432%. Interest theory writes this relationship as (1 + i) = (1 + i(4)/4)^4.