Question

Present and future value tables of $1 at 3% are presented below:

Micro Brewery borrows $240,000 to be repaid in equal installments over a period of seven years. The loan payments are semiannual with the first payment due in six months, and interest is at 6%. What is the amount of each payment?

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Present and future value tables of $1 at 3% are presented below:

N	FV $1	PV $1	FVA $1	PVA $1	FVAD $1	PVAD $1
1	1.03000	0.97087	1.0000	0.97087	1.0300	1.00000
2	1.06090	0.94260	2.0300	1.91347	2.0909	1.97087
3	1.09273	0.91514	3.0909	2.82861	3.1836	2.91347
4	1.12551	0.88849	4.1836	3.71710	4.3091	3.82861
5	1.15927	0.86261	5.3091	4.57971	5.4684	4.71710
6	1.19405	0.83748	6.4684	5.41719	6.6625	5.57971
7	1.22987	0.81309	7.6625	6.23028	7.8923	6.41719
8	1.26677	0.78941	8.8923	7.01969	9.1591	7.23028
9	1.30477	0.76642	10.1591	7.78611	10.4639	8.01969
10	1.34392	0.74409	11.4639	8.53020	11.8078	8.78611
11	1.38423	0.72242	12.8078	9.25262	13.1920	9.53020
12	1.42576	0.70138	14.1920	9.95400	14.6178	10.25262
13	1.46853	0.68095	15.6178	10.63496	16.0863	10.95400
14	1.51259	0.66112	17.0863	11.29607	17.5989	11.63496
15	1.55797	0.64186	18.5989	11.93794	19.1569	12.29607
16	1.60471	0.62317	20.1569	12.56110	20.7616	12.93794

    
Shelley wants to cash in her winning lottery ticket. She can either receive five, $194,000 semiannual payments starting today, or she can receive a single-amount payment today based on a 6% annual interest rate. What is the single-amount payment she can receive today?

Answer 1

Answer to Question 1:

Amount borrowed = $240,000
Annual interest rate = 6%
Semiannual interest rate = 3%
Number of payments = 14

Annual payment * PVA of $1 (3%, 14) = $240,000
Annual payment * 11.29607 = $240,000
Annual payment = $21,246.33

Answer to Question 2:

Semiannual payment = $194,000
Number of payments = 5
Annual interest rate = 6%
Semiannual interest rate = 3%

Single payment = $194,000 * PVAD of $1 (3%, 5)
Single payment = $194,000 * 4.71710
Single payment = $915,117.40