FDNBUSM 04 · Annuity Due and Payment Timing — Hard Exam
Conventions
Independent original practice cases. Amounts are Philippine pesos (PHP); enter numeric answers without currency symbols. Use the stated interest and payment timing. j is a nominal annual rate, i an effective payment-period rate, n the number of payments, and t years. Payment and compounding periods coincide unless stated otherwise. The factors are a(i,n) = [1 − (1 + i)^−n]/i and s(i,n) = [(1 + i)^n − 1]/i; at i = 0 both equal n. Keep full calculator precision and round money to 2 decimals only at the end; numeric money tolerance is PHP 0.02. Percentage answers are in percent, not decimal form. Report percentage and fractional-period/year answers to at least four decimal places unless exact; whole payment-count answers remain integers. Ignore taxes, fees and rounding of actual bank installments unless explicitly given. The Week 8 syllabus lists Annuities and Sinking Funds for Quiz 2; an exact calendar date was not verified.
Questions
01PHP 3,000 is deposited at the beginning of each month for 12 months, starting now. At 1% monthly, find balance at month 12, one month after deposit 12.
- PHP 38,047.51
- PHP 36,000.00
- PHP 41,427.98
- PHP 38,427.98
02Twelve PHP 3,000 deposits occur at months 0–11 at 1% monthly. Find balance immediately AFTER deposit 12, at month 11.
- PHP 34,700.50
- PHP 36,000.00
- PHP 38,047.51
- PHP 38,427.98
03A purchase is settled by 18 monthly PHP 5,000 installments, first paid immediately. At 1% monthly, what is the full cash price immediately before installment 1?
- PHP 90,000.00
- PHP 82,811.26
- PHP 81,991.34
- PHP 87,811.26
04A PHP 150,000 amount immediately BEFORE the first payment is settled by 24 equal due installments at 1% monthly. What is R?
- PHP 6,991.11
- PHP 7,061.02
- PHP 6,250.00
- PHP 5,561.02
05For the PHP 150,000, 24-payment due loan at 1% monthly, what balance remains just AFTER payment 8, made at month 7? Use unrounded R.
- PHP 103,923.21
- PHP 108,797.41
- PHP 94,071.12
- PHP 102,894.27
06An annuity-due loan has 24 equal installments R at periodic rate i, first paid at time 0. Which expression gives the balance just BEFORE payment 8?
- R a(i,17)
- R a(i,16)/(1 + i)
- R + R a(i,16)
- R a(i,16)
07An account must hold PHP 250,000 at month 24. Equal deposits are made at months 0–23 at 1% monthly. What deposit is required?
- PHP 8,764.05
- PHP 9,176.60
- PHP 9,268.37
- PHP 10,416.67
08Four PHP 12,000 annual payments occur at years 3–6. Using an annuity-due factor at 8%, which expression values them at year 0?
- 12,000 a(.08,4)(1.08)/(1.08)^3
- 12,000 a(.08,4)(1.08)/(1.08)^2
- 12,000 a(.08,4)/(1.08)^3
- 12,000 s(.08,4)(1.08)
09A single payment of PHP 10,000 is due immediately. Its present value is PHP 10,000. What periodic interest rate is implied by these two facts alone?
- 0% only
- 100%
- 10%
- The rate cannot be identified.
10Twelve equal payments at months 0–11 and twelve equal payments at months 1–12 are valued at month 0 at the same positive monthly rate. Which statement is correct?
- The earlier stream has lower PV.
- The earlier stream has an extra payment.
- The earlier stream has PV equal to (1 + i) times the later stream.
- They have the same PV because payment counts match.