FDNBUSM 02 · Compound Interest and Equivalent Rates — 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 90,000 is invested for three years at 8% nominal compounded quarterly. What is the accumulated value?
- PHP 95,508.72
- PHP 114,141.76
- PHP 113,374.08
- PHP 111,600.00
02An account quotes 12% nominal compounded monthly. What effective annual rate does it earn?
- 12.6825%
- 12.0000%
- 1.0000%
- 12.3600%
03Which investment earns more over one year: A at 10% nominal monthly, or B at 10.4% effective annually?
- B; A earns exactly 10%
- They are equivalent
- Insufficient information without a principal
- A; its EAR is about 10.4713%
04What deposit today funds PHP 150,000 due in two years at 8% effective annual interest?
- PHP 138,888.89
- PHP 174,960.00
- PHP 128,600.82
- PHP 126,000.00
05An investment doubles at 9% nominal compounded monthly. If the target must be reached at a complete month end, how many months are required?
- 8 months
- 93 months
- 92 months
- 89 months
06PHP 20,000 is due now and PHP 30,000 in two quarters. At 2% per quarter, what one payment at quarter 4 replaces them?
- PHP 52,860.64
- PHP 54,121.61
- PHP 52,020.00
- PHP 50,000.00
07A monthly-payment contract states 12% nominal compounded quarterly. Which effective rate should a monthly annuity use?
- .12/12
- .12/4
- (1.12)^(1/12) − 1
- (1.03)^(1/3) − 1
08PHP 50,000 becomes PHP 60,000 after two years, compounded semiannually. What nominal annual rate is implied?
- 20.0000%
- 4.6635%
- 9.3270%
- 10.0000%
09For a positive single sum at fixed nominal annual rate, which change increases the one-year accumulated value?
- Lowering the nominal rate
- Increasing compounding frequency
- Increasing the present-value divisor without changing time
- Replacing compound accumulation with simple interest
10A project requires PHP 42,000 in one year and PHP 58,000 in three years. At 7% effective annual interest, what reserve now covers both?
- PHP 86,597.61
- PHP 81,629.79
- PHP 93,457.94
- PHP 100,000.00