Question
In: Finance
Which of the following options regarding a $200,000 mortgage, compounded semi-annually results in the lowest total...
Which of the following options regarding a $200,000 mortgage, compounded semi-annually results in the lowest total interest payment?
A 3.5% interest rate, paid bi-weekly and amortized over 20 years
A 3.5% interest rate, paid monthly and amortized over 20 years
A 3.25% interest rate, paid monthly and amortized over 22 years
A 4% interest rate, paid monthly and amortized over 15 years
Solutions
Expert Solution
Answer is:
A 4% interest rate, paid monthly and amortized over 15 years
Please rate.
Calculations are below:
Total interest on:
A 3.5% interest rate, paid bi-weekly and amortized over 20 years:
| Payment | = | [P × R × (1+R)^N ] / [(1+R)^N -1] | |
| Using the formula: | |||
| Loan amount | P | $ 200,000 | |
| Rate of interest per period: | |||
| Annual rate of interest | 3.500% | ||
| Frequency of payment | = | Once in 0.5 month period | |
| Numer of payments in a year | = | 12/0.5 = | 24 |
| Rate of interest per period | R | 0.035 /24 = | 0.1458% |
| Total number of payments: | |||
| Frequency of payment | = | Once in 0.5 month period | |
| Number of years of loan repayment | = | 20.00 | |
| Total number of payments | N | 20 × 24 = | 480 |
| Period payment using the formula | = | [ 200000 × 0.00146 × (1+0.00146)^480] / [(1+0.00146 ^480 -1] | |
| Payment | = | $ 579.67 |
| Total interest pay: | ||
| Total payments | = | 579.67 × 480 |
| $ 278,241.60 | ||
| Less principle amount | $ 200,000.00 | |
| Interest payment- Finance charge | $ 78,241.60 |
Total interest paid on:
A 3.5% interest rate, paid monthly and amortized over 20 years
| Payment | = | [P × R × (1+R)^N ] / [(1+R)^N -1] | |
| Using the formula: | |||
| Loan amount | P | $ 200,000 | |
| Rate of interest per period: | |||
| Annual rate of interest | 3.500% | ||
| Frequency of payment | = | Once in 1.0 month period | |
| Numer of payments in a year | = | 12/1 = | 12 |
| Rate of interest per period | R | 0.035 /12 = | 0.2917% |
| Total number of payments: | |||
| Frequency of payment | = | Once in 1.0 month period | |
| Number of years of loan repayment | = | 20.00 | |
| Total number of payments | N | 20 × 12 = | 240 |
| Period payment using the formula | = | [ 200000 × 0.00292 × (1+0.00292)^240] / [(1+0.00292 ^240 -1] | |
| Payment | = | $ 1,159.92 | |
| Total interest pay: | |||
| Total payments | = | 1159.92 × 240 | |
| $ 278,380.80 | |||
| Less principle amount | $ 200,000.00 | ||
| Interest payment- Finance charge | $ 78,380.80 |
Total interest paid on:
A 3.25% interest rate, paid monthly and amortized over 22 years
| Payment | = | [P × R × (1+R)^N ] / [(1+R)^N -1] | |
| Using the formula: | |||
| Loan amount | P | $ 200,000 | |
| Rate of interest per period: | |||
| Annual rate of interest | 3.250% | ||
| Frequency of payment | = | Once in 1.0 month period | |
| Numer of payments in a year | = | 12/1 = | 12 |
| Rate of interest per period | R | 0.0325 /12 = | 0.2708% |
| Total number of payments: | |||
| Frequency of payment | = | Once in 1.0 month period | |
| Number of years of loan repayment | = | 22.00 | |
| Total number of payments | N | 22 × 12 = | 264 |
| Period payment using the formula | = | [ 200000 × 0.00271 × (1+0.00271)^264] / [(1+0.00271 ^264 -1] | |
| Payment | = | $ 1,061.39 | |
| Total interest pay: | |||
| Total payments | = | 1061.39 × 264 | |
| $ 280,206.96 | |||
| Less principle amount | $ 200,000.00 | ||
| Interest payment- Finance charge | $ 80,206.96 |
Total interest paid on:
A 4% interest rate, paid monthly and amortized over 15 years
| Payment | = | [P × R × (1+R)^N ] / [(1+R)^N -1] |
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