FDNBUSM 06 · Quiz 2 Integration — Hard Exam
6concepts
18calculations
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. This is original independent practice, not an official or recalled exam. Suggested attempt: 90 minutes, followed by written correction of every missed timeline.
Questions
01A PHP 240,000 machine requires PHP 40,000 down now and 30 equal month-end installments. Financing is 12% nominal compounded monthly. What is each financed installment?
- PHP 6,666.67
- PHP 7,749.62
- PHP 9,299.55
- PHP 5,749.62
02A PHP 250,000 loan uses 36 equal ordinary monthly installments at 1% monthly. Just after installment 10, the borrower makes an EXTRA PHP 20,000 principal payment and keeps the remaining 26 due dates. Find the recalculated installment.
- PHP 10,089.84
- PHP 8,303.58
- PHP 7,426.20
- PHP 7,639.29
03Six equal annual PHP 18,000 payments occur at years 2–7. At 7% effective annual interest, what is their time-0 present value?
- PHP 74,939.05
- PHP 85,797.71
- PHP 128,759.23
- PHP 80,184.78
04A PHP 160,000 loan at 1% monthly uses 24 equal month-end payments. Find total interest in the final 10 installments immediately AFTER payment 14. Use theoretical unrounded payments.
- PHP 3,982.01
- PHP 75,317.56
- PHP 71,335.55
- PHP 16,000.00
05A savings plan receives PHP 2,000 at each month end for 12 months, then PHP 3,000 at each month end for the next 12 months. Yield is 1% monthly throughout. Find the month-24 balance.
- PHP 91,994.44
- PHP 66,629.43
- PHP 63,412.52
- PHP 67,433.66
06Extension: twelve month-end payments of PHP 4,000 are discounted under a 12% nominal annual rate compounded quarterly. Which PV expression uses the correct monthly rate?
- 4,000 a(.03,12)
- 4,000 a(.12,12)
- 4,000 a((1.03)^(1/3) − 1, 12)
- 4,000 a(.01,12)
07A PHP 120,000 loan at 1% monthly receives 18 ordinary installments of PHP 6,000 and a balloon ADDED to installment 18. Find that additional balloon.
- PHP 12,000.00
- PHP 21,610.39
- PHP 35,537.70
- PHP 25,849.21
08An ordinary loan balance just BEFORE installment 9 is PHP 87,500. Installment 9 is PHP 4,200, and the periodic rate is 1%. What is the balance immediately AFTER installment 9?
- PHP 83,300
- PHP 84,175
- PHP 88,375
- PHP 91,700
09Fifteen PHP 4,000 due deposits occur at months 0–14. The account earns 1% monthly. Find balance at month 18, four months AFTER the final deposit.
- PHP 79,243.58
- PHP 67,001.98
- PHP 66,338.59
- PHP 67,672.00
10A buyer pays a SEPARATE PHP 12,000 down payment now plus 12 monthly PHP 5,000 installments, the first also paid now. At 1% monthly, find full cash price.
- PHP 73,838.14
- PHP 56,838.14
- PHP 68,838.14
- PHP 68,275.39
11A contract finances PHP 100,000 immediately BEFORE its first of 20 due monthly installments at 1% monthly. What principal remains immediately AFTER that first installment?
- PHP 95,513.34
- PHP 95,000.00
- PHP 94,458.47
- PHP 94,513.34
12A 24-payment due loan has monthly installment PHP 7,000 at 1% monthly. Find liability just BEFORE installment 20, made at month 19.
- PHP 34,313.76
- PHP 27,313.76
- PHP 33,974.02
- PHP 34,656.90
13Equal deposits of PHP 2,500 occur at each month BEGINNING, starting now. The fund earns 1% monthly. What is the smallest whole n so the balance at month n is at least PHP 50,000, with n deposits at months 0 to n−1?
- 21 deposits
- 19 deposits
- 18 deposits
- 20 deposits
14At a positive rate, an ordinary stream and a due stream have the SAME payment count and SAME installment. Their standard future values are compared at the same time n. Which difference formula is correct?
- F_due − F_ordinary = R
- F_due − F_ordinary = F_ordinary/i
- F_due − F_ordinary = i F_ordinary
- F_due − F_ordinary = iR
15Annuity-due PV is used to value a stream first paid at year 4. The due factor gives its value at year 4 immediately before that payment. Which extra movement obtains value at year 1?
- Discount four annual periods.
- Discount two annual periods.
- Accumulate three annual periods.
- Discount three annual periods.
16A savings plan has 18 due monthly deposits. For an amount measured immediately AFTER the eighteenth deposit, which final-payment growth exponent applies?
- 0
- 1
- 17
- 18
17A reserve targets PHP 500,000 at quarter 16. PHP 80,000 is invested immediately, then 16 equal QUARTER-BEGINNING deposits occur at quarters 0–15, at 2% quarterly. Find each periodic deposit.
- PHP 26,299.08
- PHP 20,522.60
- PHP 20,933.05
- PHP 22,091.23
18A fund receives ten year-end deposits of PHP 20,000. It earns 4% for years 1–5 and 6% for years 6–10. Find balance just after deposit 10.
- PHP 263,615.90
- PHP 221,068.31
- PHP 257,707.09
- PHP 251,557.85
19A PHP 8,000 ordinary deposit scheduled at year 3 is missed. It is replaced at year 5 in a fund earning 5% annually. What replacement amount restores the original future-value path?
- PHP 8,000.00
- PHP 7,256.24
- PHP 9,261.00
- PHP 8,820.00
20A PHP 1,000,000 interest-only debt charges 8% annually and is due after 10 years. Its separate reserve receives end-of-year deposits and earns 5%. What is the annual interest PLUS reserve deposit?
- PHP 159,504.57
- PHP 180,000.00
- PHP 149,029.49
- PHP 79,504.57
21At quarter 9 just after the deposit, actual fund is PHP 190,000. Target is PHP 600,000 at quarter 21. Future yield drops to 1% quarterly. What new quarter-end deposit is needed?
- PHP 47,309.27
- PHP 30,428.00
- PHP 32,328.00
- PHP 15,742.61
22A fund starting from zero has end-of-quarter deposits R and quarterly yield i. Which statement about its period-k increase is correct?
- Increase = i × closing balance + R
- Increase = iR only
- Increase = i × opening balance + R
- Increase always equals R only
23A debt has contractual principal PHP 700,000 and a separate accumulated sinking fund of PHP 280,000. Which statement is accurate before the fund is applied to the debt?
- Contractual principal is automatically PHP 420,000.
- The reserve earns interest on PHP 700,000.
- Both principal and reserve are PHP 420,000.
- Contractual principal is PHP 700,000; net unfunded amount is PHP 420,000.
24A fund targets PHP 150,000 at year 5. Actual balance just after deposit 4 is PHP 113,500. Final-year yield is 4%. What adjusted deposit at year 5 exactly reaches the target?
- PHP 31,960
- PHP 36,500
- PHP 32,500
- PHP 30,000