FDNBUSM 03 · Ordinary Annuities and Loan Balances — 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 4,000 is deposited at each month end for 18 months at 6% nominal compounded monthly. What is the balance immediately after deposit 18?
- PHP 75,143.15
- PHP 75,518.87
- PHP 72,000.00
- PHP 78,762.88
02An appliance requires PHP 20,000 now and 24 month-end installments of PHP 6,000. At 1% effective monthly interest, what is its equivalent cash price?
- PHP 127,460.32
- PHP 164,000.00
- PHP 181,840.79
- PHP 147,460.32
03PHP 180,000 is repaid in 36 equal month-end installments at 12% nominal compounded monthly. What is the theoretical installment?
- PHP 6,800.00
- PHP 4,178.58
- PHP 5,978.58
- PHP 5,000.00
04A PHP 180,000 loan uses 36 equal month-end installments, first due in one month, at 1% monthly. Find balance immediately after installment 12. Use the unrounded theoretical installment.
- PHP 143,485.82
- PHP 127,005.20
- PHP 131,667.10
- PHP 108,257.09
05Four PHP 12,000 annual payments occur at years 3–6. At 8% annually, what is their PV at year 0?
- PHP 34,075.38
- PHP 31,551.28
- PHP 39,745.52
- PHP 54,073.34
06A PHP 200,000 loan at 1% monthly requires 24 ordinary installments plus an additional PHP 50,000 balloon with installment 24. Find each regular installment.
- PHP 9,414.69
- PHP 7,061.02
- PHP 11,268.37
- PHP 7,561.02
07A 36-payment ordinary loan at 1% monthly has installment R. Which expression is the balance immediately BEFORE payment 12?
- R a(.01,25)
- R s(.01,12)
- R + R a(.01,24)
- R a(.01,24)
08PHP 5,000 is deposited at every month end at 1% monthly. What minimum whole number of deposits reaches PHP 100,000?
- 21
- 19
- 18
- 20
09A loan of PHP 100,000 charges 1% monthly. The proposed month-end payment is PHP 900. Under this fixed-rate model, which conclusion follows?
- The debt does not amortize because payment is below first-month interest.
- The debt is cleared in 112 months
- The debt is cleared in 100 months
- The loan has no interest because payment is too small
10A PHP 150,000 loan at 9% nominal compounded monthly is repaid by 30 equal month-end installments. What is the principal portion of installment 1?
- PHP 5,602.22
- PHP 1,125.00
- PHP 5,000.00
- PHP 4,477.22